Nicolas Otamendi is a Manchester City player after the Premier League club and Valencia confirmed the transfer.
No fee is revealed by either party but reports from Spain had previously put the cost of the transfer at €45m.
City originally wanted to send Eliaquim Mangala to Mestalla in part-exchange but the French defender opted to stay at the Etihad Stadium after regaining the trust of manager Manuel Pellegrini.
“Valencia have reached an agreement with Manchester City for the transfer of Nicolas Otamendi,” the statement on Valencia's official website begins.
“We would like to wish Otamendi the best of luck in his new career.”
City meanwhile have confirmed Otamendi has signed a five-year contract and will wear the No 30 shirt.