The Sevilla winger had been strongly linked with the Premier League outfit, which made the 27-year-old Spain international one of its top targets this summer.
The Liga club announced on itsr website that the 27-year-old will move to Etihad Stadium subject to a medical, while the fee is believed to be in the region of 25 million euros.
City, which is expected to appoint Manuel Pellegrini as its next manager after he revealed that he has a verbal agreement with the Premier League club, had made Navas a key target this summer.
Navas also added fuel to the speculation, recently admitting his admiration for the club.
"I like Manchester City a lot and it has great players," he told reporters. "I'm open to anything. I want to win more and reach my goals. Manchester City has done all it can to bring me in, and I have to be grateful for that.
"I want to go on and win trophies."
Navas has spent his entire career at Sevilla, making his debut in November 2003. He played 393 times for the Andalusian side, winning two UEFA Cups, one European Super Cup, two Copa del Reys and a Spanish Super Cup.