Sevilla had already said last week that the 27-year-old would be leaving the club to join up with international team-mate David Silva at the Etihad Stadium and now the English club have confirmed the deal.
"Manchester City is an exciting project and this is the right moment for me to take this step. I'm very happy with the opportunity and the decision," Navas said on his new club's website.
"The Premier League is a competition where the football is very fast and will suit the way I play. I'm really looking forward to it.
"I'm going to a great club in England and I want to continue developing my game there. The club has put a lot of faith in me and I want to repay them out on the pitch."
Navas, who spent 10 seasons with Sevilla, joins a trophy-hungry club who are determined to improve on last season's showing where they finished runners-up to Manchester United in the league and lost to Wigan Athletic in the FA Cup final.
Despite still not having appointed a new manager after last month's sacking of Roberto Mancini, they have been busy bolstering their squad for next term and last week signed Brazil midfielder Fernandinho from Shakhtar Donetsk.
Former Malaga, Villarreal and Real Madrid manager Manuel Pellegrini is widely expected to be named as Mancini's successor after the Chilean said last month he had a verbal agreement with the club.
He overcame his anxiety to help the Iberian nation win their first World Cup in 2010 and was part of the squad that defended Spain's European crown last year.
