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7 year oldThe 23-year-old France left-back has signed a five-year deal.
Mendy is City's fifth major signing of the summer, taking their spending to more than £200m.
"He is undoubtedly one of the world's best full-backs, our number one target in this position," said director of football Txiki Begiristain.
Mendy played 34 times for Monaco last season and helped them to their first Ligue 1 title in 17 years after joining them from Marseille last summer.
City have already signed England right-back Kyle Walker for £45m, plus a potential £5m of add-ons, Portugal midfielder Bernardo Silva (£43m), Brazilian keeper Ederson Moraes (£35m) and defender Danilo from Real Madrid (£26.5m).
They have sold left-back Aleksandar Kolarov, 31, to Roma for £4.5m.
The arrival of Mendy leaves Manchester City with the most expensive defensive line-up in world football.
When Ederson moved to the club from Benfica earlier this summer, his move was a world record for a keeper in sterling, although not in euros.
Mendy and Walker have been added to a backline which also includes centre-back John Stones, who was bought for £47.5m from Everton last summer,with the trio making up three of the world's five most expensive defenders.
Central defenders Nicolas Otamendi and Eliaquim Mangala, who spent last season on loan at Valencia, also joined City for fees believed to be in the region of £32m.
Monaco beat Paris-St Germain to the French title last season and also reached the Champions League semi-finals.
Their players have subsequently been in demand, and Mendy is the third major departure from the Ligue 1 club so far this summer.
Silva and Mendy have both joined City, while Chelsea signed midfielder Tiemoue Bakayoko.
They could yet lose more players, with striker Kylian Mbappe, winger Thomas Lemar and defender Fabinho linked with moves.
Julien Laurens, French football expert
What can City fans expect? Very much what they saw when he faced him in the Champions League. That really was the time where people at City saw how good he was. He had an incredible last 18 months, especially last season with Monaco.
He's still young and he's got the engine to go up and down the left-hand side through the whole match. The quality of his crossing is fantastic. He is such a strong and quick player.
Defensively he needs to improve his positioning. Sometimes he tends to switch off a little bit - but I think Pep can sort that out.
Defensively, you won't see the amazing tackles Mats Hummels did for Bayern, or some great positioning play. That's not him.
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