The 23-year-old is set to join Pep Guardiola-coached side on contract until 2023 after the Manchester giants bought out his release clause form the Basque club, reports Efe.
"I am very happy to be here. City are a club with a lot of ambition and they are one of the best teams in Europe," said the French defender in a statement relayed by the English club.
"I am looking forward to working under Pep Guardiola and trying to help the club achieve success," he added.
Laporte scored 10 goals in his 222 appearances for Athletic Bilbao.
Guardiola said Laporte, who is set to wear the number 14 shirt, could start playing with the Sky Blues straight away.
"He's played since a young age in La Liga, so at a high level. He's strong in the air and fast. He's got good quality and we are delighted," Guardiola said of the club's latest purchase.
The Catalan coach also announced that the club's German winger Leroy Sane would be sidelined for up to six weeks with an ankle ligament injury sustained during the FA Cup tie against Cardiff City.
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