The 20-year-old England international's transfer is a record fee for an English player and he also becomes City’s record signing.
Sterling, who will fly out to meet his new team-mates in Australia within the next 24 hours, will wear the No.7 shirt.
A versatile, attacking midfielder, Sterling began his career at Queens Park Rangers before joining Liverpool as a 15-year-old in 2010 for an initial fee of £600,000.
He made his debut aged 17 against Wigan Athletic in 2012 and went on to make 129 appearances for the Reds, scoring 23 goals.
In 2014 he became only the second English player to win the Golden Boy award – an honour bestowed by European sports journalists on the Under-21 player who has had the most impressive season – with previous winners including Lionel Messi, Sergio Aguero, Isco and Paul Pogba.
A 2015 professional study by Soccerex recently rated Sterling as the most valuable young player in Europe
Raheem also won back-to-back Liverpool FC Young Player of the Year awards for the 2013/14 and 2014/15 campaigns.
Manager Manuel Pellegrini said: “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.
“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."
Watch out for an exclusive CityTV interview with Raheem coming up on mcfc.co.uk including the Blues’ new No.7’s first words as a City player.
Don't forget if you want to see Raheem up close and personal, he will join the rest of the squad at this year's City Live in August.Tickets available
so don't miss out.