The 27-year old Spain international has passed a medical in New York which sees his £14.9million move from Sevilla now complete.
"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," he 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."
During his time with Sevilla, which lasted more than 13 years, Navas helped the Andalusia club take out two UEFA Cups, one UEFA Super Cup and two Copa del Reys.