The 27-year-old has signed a five-year contract although no financial details of the transfer were released.
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 website, www.mcfc.co.uk: “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 most important. To be here inside a club that looks so wonderful from the outside is a dream.”
Valencia were believed to be hoping to use the sale of the player to write off part of the fee they still owe City for striker Alvaro Negredo.
Otamendi joined the Spanish club from Porto just a year ago. Initial reports at the weekend claimed Valencia wanted to offset his loss by signing Mangala on loan in exchange but City had no intention of allowing the Frenchman to leave Eastlands.
City manager Manuel Pellegrini said: “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.
Otamendi has 25 caps for Argentina and was a member of the side that reached the Copa America final in the summer alongside new City team-mates Demichelis, Sergio Aguero and Pablo Zabaleta. – AFP
Original source: City strengthens defence