The move will see PSA regain its position as Europe’s second-largest automobile manufacturer, after Germany’s Volkswagen, the source said on Friday. That position is currently held by rival French automaker Renault.
The negotiations, revealed last month, were “swiftly concluded,” the source added.
The deal “will be sealed on Monday morning in France and in Germany,” the source said, adding that both sides “were very enthusiastic and satisfied.”
The planned takeover of the Opel division by PSA, which owns the Peugeot and Citroen brands, was unveiled in the middle of February.
It sparked fears in Germany and Britain that the prospective new owner could cut non-French jobs.
PSA boss Carlos Tavares had said earlier he wanted to develop the “iconic” Vauxhall brand as “part of Britain’s automobile sector heritage”.
Vauxhall employs around 5,000 people in Britain. Opel operates some 10 factories in Europe spread across six countries, and had 35,600 employees at the end of 2015, 18,250 of them in Germany.
Founded in 1862, Opel, with its lightning-bolt emblem, is a familiar sight on German and European roads.
– ‘Lucrative for shareholders’ –
But in recent years the firm has booked repeated losses, costing Detroit-based GM around $15 billion (14 billion euros) since 2000.
A sharp fall in the pound since Britain’s vote to quit the EU last June sank Opel’s hopes of getting back into the black in 2016, and it ended up reporting a loss of $257 million.
Britain, where it sells vehicles under the Vauxhall brand, is Opel’s largest European market.
PSA has been active in trying to win backing for the acquisition, with chief executive Tavares last week securing the support of Germany’s Chancellor Angela Merkel and also holding a phone conversation with British Prime Minister Theresa May.
France’s CGT union late Friday said the deal would be “very lucrative for PSA shareholders” and issued a warning to the PSA and Opel employees.
“Once German elections (in September) have taken place, it is obvious that Carlos Tavares will have as first objective to attack employment”, it said.
Tavares has said the group would respect the commitments made by GM, namely a rejection of short-term economic redundancies and a promise to invest in sites until 2020.
In talks last week with the head of Britain’s biggest trade union, Len McCluskey, he “repeated his commitment to dialogue under existing agreements and the PSA group’s ethical approach”.
Britain’s plans to quit the European Union have created uncertainty across the business world, particularly in the car sector which is dependent on imports and exports with the European Union.
PSA last month said net profit for 2016 rose 79 percent to 2.15 billion euros ($2.27 billion) with the auto giant pledging to pay shareholder dividends for the first time since 2011 to the tune of 0.48 euros per share.
PSA’s improved profitability comes despite a decline in sales due to the scope of consolidation and foreign exchange effects.