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."
The club did not give details of the length of contract or transfer fee but local media reported it to be in the region of 15 million pounds.
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.
The wealthy club, who won the Premier League in 2012 and FA Cup in 2011, have made no secret of their ambitions with chief executive Ferran Soriano saying last month that City wanted to win five trophies in the next five years.
That search for silverware could be helped by the addition of Navas, who has been tormenting defenders with his electric runs down the right wing since making his top-flight debut for Sevilla in 2003.
He was a key part of the team who won the UEFA Cup in 2006 and 2007 but was unable to take up a place in the Spain squad for many years due to fears about travelling away from his Andalusian home.
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.
Despite his slight frame, he is a tenacious tackler and ball winner but has been criticised at times for a lack of goalscoring prowess and did not find the net at all for Sevilla in 37 La Liga appearances last season.
He has made 23 appearances for Spain, scoring two goals.
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