The 23-year-old England player, who has seven goals in 14 games this season, said he was in the best place to improve, having played in several positions under Pep Guardiola.
British media said Sterling's deal was worth up to 300,000 pounds ($389,000) a week, which would put him among the best paid players in the league.
“I’m delighted to sign," he told the City website https://www.mancity.com/news/first-team/first-team-news/2018/november/raheem-sterling-manchester-city-contract-extension-news. "My development here has been incredible.
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"I felt from the minute I got here it was the right choice for me. It’s paid off and I’m really grateful.”
Sterling joined City from Liverpool for 49 million pounds in 2015 and won the league title and League Cup last season.
“This is a significant moment for the Club," added City's Director of Football Txiki Begiristain.
"Raheem has improved dramatically in the past two seasons and is now one of the Premier League’s best attacking players. His statistics tell their own story.
“He’s quick, strong and excellent in front of goal – everything a modern-day forward needs to excel. We’re all delighted he has committed his future to City.”
(Writing by Ken Ferris; Editing by Ed Osmond)
