Navas has penned a four-year contract with the Premier League club.
"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."
Navas joined Sevilla as a trainee in 2000 before signing his first professional deal three years later.