The England winger signed a five-year deal at City after forcing his way out of Anfield following several fractious months, during which he rejected a new contract and publicly questioned the club's ambitions.
"I'm just glad it's all over and done with and I can't wait to get on the training field," the 20-year-old Sterling told City's website. "The thing that excites me the most is the world-class squad we have and knowing we have a team that is capable of winning things year in, year out.
"The more quality players that are around you, the more quality it brings out in you, so I can't wait to get started and play alongside them."
The transfer fee eclipses the previous record for an English player - 35 million pounds (then $56 million) - which Liverpool paid Newcastle for striker Andy Carroll in 2011.
Although Sterling only made his Premier League debut three years ago, City believes the skilful, quick forward, is already a top talent and worth breaking the record for. Sterling is an established member of the England team after making his debut in 2012, scoring once in 16 appearances.
"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 from the pre-season tour.
"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."
Sterling leaves Liverpool after scoring 23 goals in 129 appearances but without any winners' medals.
Sterling came close to winning the Premier League in 2014 but Liverpool lost out to City and faltered last season to finish sixth, never looking like winning the title for the first time since 1990.
City's 2014 title was its second Premier League success since the club's fortunes were transformed by the influx of Abu Dhabi investors in 2008.
Breaching UEFA's Financial Fair Play rules led to limits on City's spending last year, but those restrictions have been lifted after losses were cut at the Etihad Stadium - enabling the club to invest so much in signing Sterling.
Sterling joined Liverpool aged 15 from the Queens Park Rangers academy and the London club is reported to be due a 20 per cent cut of City's payment to Liverpool under the terms of that 2010 deal.
Liverpool marked the loss of its leading talent with a terse 32-word statement on its website, which ended by saying it "wishes Raheem well."
Liverpool manager Brendan Rodgers insisted on Monday, though, that there are no hard feelings between him and Sterling - despite the player agitating for a move and refusing to go to Thailand on the pre-season tour.
"I want to thank Brendan Rodgers for giving me ... a real chance to cement a place in the first team and show the world my talents," Sterling said.