Chelsea manager Luiz Felipe Scolari told the club he only wanted to work with 23-24 first-team players this season and used the England international sparingly in pre-season.
The winger was left out of the squad in the victory at Wigan on Sunday and his departure paves the way for Brazil star Robinho to arrive at Stamford Bridge from Real Madrid.
Wright-Phillips, 26, who was also wanted by Portsmouth and Everton, was signed by former manager Jose Mourinho in 2005.
But he started just 43 League games for Chelsea and scored a total of only 10 goals in his three years at the club.
It is understood Wright-Phillips has agreed a deal worth around £70,000 a week, which is the same wages he was on at Chelsea.
The winger will quickly get a chance to come up against his old team-mates when City take on Chelsea at Eastlands on 13 September.
With the player gone, chief executive Peter Kenyon will step up his attempts to buy Robinho.
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