The winger had been strongly linked with the Premier League outfit, who have made the 27-year-old Spain international their first summer capture
The Liga club announced on their website that the 27-year-old will move to the Etihad Stadium subject to a medical, whilst the fee is believed to be in the region of €25 million (£21.3m).
City, who are expected to appoint Malaga boss Manuel Pellegrini after he revealed that he has a verbal agreement with the Premier League club, had made the winger a key target this summer.
Navas also added fuel to the speculation after 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 Rey titles and a Spanish Super Cup.