The Premier League leaders met the 23-year-old’s £57.2m release clause last week in a deal which makes him City’s record signing. They paid £55m for Kevin De Bruyne in 2015.
Laporte has been with Athletic since 2012. He has played for various of France’s age-group teams and was called into the senior squad last year but did not get game time.
“I am very happy to be here,” said Laporte. “City are a club with a lot of ambition and they are one of the best teams in Europe. I am looking forward to working under Pep Guardiola and trying to help the club to achieve success. It means a lot that the club have shown faith in me and I am excited to get started.”
Laporte, who has agreed a deal to join City until 2023, becomes Pep Guardiola’s sixth signing of the season.
“We have assessed defensive options and he is a player we have admired for a long time,” said Txiki Begiristain, City’s director of football. “With his quality and ability to play out from the back, we feel Aymeric will fit in perfectly with Pep Guardiola’s playing style.”