Laporte, who has already been handed the number 14 shirt, has signed a five-and-a-half year contract at the Etihad Stadium that promises to keep him at the club until the summer of 2023.
The fee surpasses the £55m deal that saw City land Kevin De Bruyne from Wolfsburg in 2015, while new Liverpool signing Virgil van Dijk (£75m) is the only defender ever to have moved with a bigger price tag anywhere in the world.
Adding Laporte to Benjamin Mendy, Kyle Walker and John Stones means that City are responsible for four of the six most expensive defenders of all time. That group are also four of City's five most expensive signings in club history, showing just how much has been invested in defenders at the Etihad over the last 18 months.
"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," Laporte told ManCity.com.
"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."
23-year-old Laporte, who is yet to make his senior international debut, was born in the Basque region of southern France and joined Athletic Bilbao's youth ranks at the age of 16. He started to become a first-team regular just two years later and leaves the club after over 220 games.
(You may also be interested in '5 Reasons for Man City Fans to Get Excited About Aymeric Laporte')