The 27-year-old, who had been strongly linked with a move to the Etihad Stadium since the weekend, has signed a five-year contract with the Barclays Premier League club.
Otamendi will bolster central defensive ranks at City that include two familiar faces in former Porto team-mate Eliaquim Mangala and international colleague Martin Demichelis, as well as captain Vincent Kompany.
Otamendi told the club’s official website: “I am here to give my best, to fight game by game and push City to the highest peaks for as long as possible, and I wish we will be able to win several cups and titles.
“That’s the most important. To be here inside a club that looks so wonderful from the outside is a dream.”
Manuel Pellegrini added: “Nicolas Otamendi was arguably the best defender in La Liga last season and so naturally I’m delighted to have added a player of his quality.
“He is an established international for one of the best nations in world football and I have no doubt that he has the right mentality to fit into a squad where he will find many familiar faces, including Eliaquim and Fernando who he played alongside in Portugal.
“As a footballer, Nicolas has all of the qualities to be a success in the Premier League – he’s strong, he’s excellent in the tackle and he’s very good technically.
“I am sure he will become another Argentine player our fans will enjoy watching.”