The 27-year-old has signed a five-year contract with the Premier League side.
City will pay an initial £28.5million for the highly-rated defender, who will link up with his Argentina teammates Sergio Aguero, Martin Demichelis and Pablo Zabaleta at Eastlands.
Otamendi told City’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.
“hat’s the most important. To be here inside a club that looks so wonderful from the outside is a dream.”
Manager 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.”