The call came through at 7.32 pm local time. Clinton offered the job, Kaine accepted, and then the former Secretary of State said: "Now, I don't want to alarm you, but John Podesta is outside your building right now".
So it was that a process begun in secret six weeks ago - that had remained a mystery throughout, even to those who were being vetted - came to its cloak-and-dagger conclusion.
"It's certainly something quite different from the usual course of affairs, particularly for someone going through it for the first time. It's this odd, in-between world - being talked about a lot, but really the process goes on within the privacy of the campaign," said Housing Secretary Julian Castro, who was under consideration.
Clinton had started with an initial list of close to 30 names, said a campaign aide, speaking on background. Each was given an initial vet, the results of which were delivered to her Chappaqua, New York, home by Podesta, the campaign chairman, shortly after the June 8 New York primary.
Podesta and longtime Clinton confidant Cheryl Mills had compiled them in binders, which he stashed in oversised plastic bags.
Though the list was long, Kaine's name had always been presumed to be near the top of it, both among those involved in the process and in the frenzied public speculation.
"There was a rhythm to this," said one person familiar with the process. "It's like a race where there are three, four or five horses moving up and moving back. Kaine was always there. ... I think there was a presumption all along."
The winnowing began, with the vetting materials being distributed to teams of lawyers from different firms. Candidates were encouraged to make frequent television and campaign appearances, with Clinton's team watching to see how well they came off in making the case for her candidacy.
Finalists were summoned to meet privately with Clinton, starting with Kaine, who had his first serious conversation with her about the vice presidency on July 15.
"Why don't you come back to the house later?" she asked him, after they appeared together at a rally in Annandale, Virginia.
The meeting at her home on Whitehaven Street - within walking distance of where Kaine will live, if she is elected - lasted an hour and a half. Podesta sat in on the beginning, then left them to themselves.
That did not become public, but a procession of others would be spotted by the media going in and out of her house over the following days.
Kaine, however, would be the only candidate called back for a second meeting with the nominee-in-waiting.
That one took place over lunch at her house in Chappaqua on July 17. Kaine brought his wife, and Clinton was joined by former President Bill Clinton, daughter Chelsea and son-in-law Marc Mezvinsky.
Once she settled on him early in the week, there would be no wavering, none of the public drama that had marked the chaotic final hours before Donald Trump formally announced his pick Indiana Governor Mike Pence.
In Clinton's case, operational security would be maintained, right up to the end. A speech was written, and a plan was hatched. Those who did not get the nod were notified of that, either by Clinton or Podesta, before she dialled Kaine.
Podesta and three aides known as the "go team" had slipped out of her Brooklyn headquarters, taking the freight lift to avoid the reporters who were staking out the front of the building.
Once they made contact with Kaine in Newport, they whisked the senator and his wife Anne Holton back to their hotel to grab their things and headed for Miami.
Aboard the flight, Kaine worked on a draft that had been written for him by speechwriter Megan Rooney, and he became better acquainted with Matt Paul, who had been Clinton's Iowa state director and will now be part of Kaine's travel team.
Podesta's chief of staff Sara Latham, who had been the keeper of the vetting books, coaxed the senator to pull out his harmonica - which he did, and played them a Beatles song. Kaine also called President Barack Obama, whom he had supported over Clinton early in the bitter 2008 Democratic presidential primary, and whose short list he had been on for vice-president eight years ago.
According to a person familiar with the weekend's schedule, the campaign did not tell staff on the ground who would be announced at the events in Tampa or in Miami - or whether someone would be announced at all. The events were planned to accommodate a number of possible running mates.
Personal chemistry is a hard thing to force, in politics just as in life. But it seemed to be there when Clinton and Kaine made their first appearance today in Miami as the Democrats' ticket for November.
Kaine was not the name on her list who had the longest and deepest relationship with Clinton, who is famous for valuing those traits. That would have been Agriculture Secretary Tom Vilsack, who has known her since the 1970s. She was instrumental in helping him win a tough race for Iowa Governor in 1998, and they have been there for each other in the trenches ever since.
Nor was affable, mild-mannered Kaine the pick who would have brought the most pizzazz to the ballot.
That might have been Senator Elizabeth Warren, the darling of the liberal left; or the charismatic Senator Cory Booker; or Housing Secretary Julian Castro and Labour Secretary Tom Perez, both Hispanics whose selection would have given the first woman to lead a major party ticket a double-down claim on making history
And yes, Kaine does represent a crucial swing state, but using a vice presidential selection to pick up favourite-son electoral votes is a gambit that has not worked since New Englander John F. Kennedy named Lyndon B. Johnson of Texas in 1960.
It needs to be someone who, whenever they walk into a room, you are glad to see them, and you want them as part of any conversationClinton, having seen the White House from the inside, knows that what she has made is a kind of marriage proposal, one that she may have to live with for as many as the next eight years.
Or as Podesta, himself a former White House chief of staff, told her last Tuesday: "It needs to be someone who, whenever they walk into a room, you are glad to see them, and you want them as part of any conversation."
And of course, someone who will be an asset in what promises to be a brutal election campaign.
Clinton had been impressed by a number of the candidates. An aide said she had particularly enjoyed events with Booker and Perez.
Warren did not expect to be picked for at least two reasons: A Republican governor in Massachusetts would be able to appoint a Republican to replace her; and a ticket with two women was widely seen as a bridge too far. Nonetheless, Warren and Clinton have developed a good relationship after a number of conversations, not all of them vice president-related, over the past weeks.
Kaine, for his part, had caught Clinton's eye during the drawn-out Democratic primary against Senator Bernie Sanders of Vermont. He made frequent appearances on her behalf, making a "very polite" argument that she was the candidate better prepared on foreign policy, a Clinton aide said.
In that first private meeting with Kaine about the job, the Clinton official added, the two talked about how they had both spent time while getting their Ivy League law degrees doing work for the disadvantaged - she giving outlet to her Methodist values working for the Children's Defence Fund, and he with the Jesuit Volunteer Corps in Honduras.
"She saw a common thread in the role that faith played in guiding both of their entries into public service," the aide said.
Some of the other contenders offered their congratulations to Clinton's pick. "KAINE IS ABLE!!!" Booker tweeted shortly after word got out.
And just having been in contention has the effect of elevating the stature of those who were talked about - as Kaine could attest from having been in contention for the job that eventually went to Vice-President Joe Biden.
"In life, the road turns and you don't know how things are going to work out and that often times things can work out for the better so I'm looking forward to the years ahead," Castro said.
Back in 2008, Tim Kaine might have been thinking the very same thing.
Vice-presidential candidates can be divided into two categories: political choices selected for what they can deliver on Election Day and governing picks who can do some heavy lifting in the White House.
By choosing Tim Kaine, Hillary Clinton will get both.
Clinton has been the favourite to win in Virginia since the Republicans chose Donald Trump, whose backing in heavily populated suburbs such as Northern Virginia should lag behind the previous three Republican presidential candidates.
But with Kaine on the ticket, Virginia can probably retire its swing-state jersey for this year. A good-size Democratic victory in this once-reliable GOP state should be expected, likely larger than President Barack Obama's 3.9 point margin in 2012. Recent studies have suggested that a solid running-mate can add two to threepercentage points in his or her home state.
Experience matters greatly to success on the campaign trail and in office, and Kaine has experience at every level. He has spent more than two decades learning local, state and federal government through service as a city council member, mayor, lieutenant governor, governor and US senator - all the while never losing an election. Even Republican politicians have acknowledged that Kaine mastered each job, and many have praised Kaine's savvy and collegiality.
Kaine's critics on the liberal side have called him boring, prompting Kaine to acknowledge this "flaw". Actually, that's true only if you consider a keen mind and intellectual rigor to be dreary. Kaine can slice and dice policy like the Harvard Law School grad he is. Plus, if there's ever been a year when we've needed less excitement, it's this one.
Naturally, there will be downsides to Kaine's nomination. Some of Bernie Sanders's voters are surely disappointed, having hoped for an outspoken liberal such as Senator Elizabeth Warren. Kaine will not shake up the race or cause people to think about Clinton in new ways. And in a year when many Americans appear dead set against long-term officeholders, Kaine's record will cut against the grain.
In this hyper-partisan era, Kaine is a bit of a throwback to the days when pols at least tried to work together. When he was elected lieutenant governor, he went to see every one of the 40 senators scattered around the state, without fanfare, to get to know them and find common ground. When he ran for governor in 2005, he hoped to continue a bipartisan approach, but Republicans in the legislature had no desire to cooperate with another Democrat, having helped the previous Democratic Governor, Mark Warner, achieve high popularity through passage of his transportation programme. Kaine was frustrated in accomplishing much of his agenda.
Yet Kaine has continued to reach out. As soon as he arrived in the Senate, he tried to make common cause with as many Republicans as he could. To an outsider, the Senate seems mainly inclined towards gridlock, but when I recently asked Kaine what proportion of his chamber was open to working together, he unhesitatingly (and optimistically) answered "75 per cent". That's where Kaine may be disappointed again as a vice-presidential nominee. Does considerable common ground exist anymore?
Kaine isn't much of an attack dog, which was widely noted in his joint appearance with Clinton last week. Kaine isn't timid, and he learned a lot about targeting opponents as the chair of the Democratic National Committee for part of Obama's term. Still, he'll never be as savage as many Democratic partisans would like. It isn't in him.
What is in him is a philosophy in clear contrast with that of his Republican counterpart, Indiana Governor Mike Pence. Both men are substantive and low-key, but Pence is a staunch conservative, while Kaine is more liberal than his reputation in progressive circles suggests. Those who call Kaine a moderate forget that his early career took place in a Virginia that was far more conservative and traditionalist than the demographically diverse state of today.
Looking at Pence's and Kaine's lengthy records, the contrast is sharp.
To the extent that Kaine focuses on Pence rather than Trump, he will be certain to make an issue of the religious freedom law Pence signed as governor, which was widely viewed as an attack on the lesbian, gay, bisexual and transgender community. Kaine has a lengthy record of backing gay rights.
The debate about climate change, where Kaine and Pence take opposite sides, is another sharp difference. The Pence-Kaine disagreements even extend to smoking. One of Kaine's proudest achievements as governor was a smoking ban in bars and restaurants; by comparison, Pence has questioned whether smoking actually causes cancer.
If Clinton wins, Kaine could be an enormously valuable vice-president. Moreover, one can easily imagine Kaine as president if it ever should prove necessary. In recent history, this hasn't always been the case with running-mates.
Like all vice-presidential candidates, and occupants of the nation's second-highest office, Kaine will have to defend some things he would never have done personally and believes are wrongheaded. The real question is whether Kaine, viewed by friends and foes as a moral, ethical person, can find his own voice within a Clinton circle that has sometimes made poor decisions and taken self-defeating shortcuts. Could Kaine do more than be a good team player by guiding Clinton to better choices?
We are about to find out - initially on the stump and maybe in the next administration. First, Kaine will have to grit his teeth and help win an unpleasant scorched-earth campaign.