Sevilla had already announced the transfer last week, but City have rubber-stamped a deal which sees Navas move to the Etihad Stadium for a fee of £14.9 million.
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“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 told the club's official 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 has won the World Cup and European Championship with Spain, came through Sevilla's youth system, scoring 34 goals in nine seasons and made 393 appearances for the club.
The Spaniard joins Fernandinho in making the move to Manchester City, and will be given a short holiday following the Confederations Cup before linking up with the rest of the squad for pre-season training.