City paid 49 million pounds for Sterling, according to media reports, with the England international signing a five-year contract at the Etihad Stadium.
The pacy winger will fly out to join his new team mates, who are on a pre-season tour in Australia.
"Raheem Sterling is one of the best attacking players in world football, and I am very much looking forward to him joining our squad out in Australia later this week," City manager Manuel Pellegrini said on the club website (www.mcfc.com).
"He is a young player with outstanding ability, and I am sure the Manchester City fans will be very excited about seeing him in action for the team."
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Abu Dhabi-owned City did not confirm the transfer fee but said it was a record for the club.
The fee is also higher than the previous record for an English player, surpassing the 35 million pounds Liverpool paid Newcastle United for target man Andy Carroll in 2011.
Sterling endured an acrimonious end to his career at Liverpool after making 129 appearances and scoring 23 goals, having moved to the Merseyside outfit from Queens Park Rangers in 2010 as a 15-year-old.
His relationship with Liverpool hit trouble in April as contract talks stalled and he gave an unauthorised interview to the BBC, denying being a "money-grabber" and claiming he was motivated purely by ambition.
His outspoken agent Aidy Ward then angered the club and its supporters in May by saying the England player would not sign a new deal at Anfield -- even for 900,000 pounds ($1.40 million) a week.
With no City deal on the immediate horizon, the issue came to a head last week as the player did not fly out with Liverpool for their pre-season tour despite being named in the squad.
Liverpool, however, showed no bitterness in a short statement confirming his departure on their website.
"Liverpool Football Club can confirm Raheem Sterling has completed a transfer to Manchester City," the club said. "Liverpool FC wishes Raheem well."
(Reporting by Toby Davis; editing by Ed Osmond/Alan Baldwin)
