The 23-year-old France international joined Monaco from Marseille at the start of the 2016/2017 season.
He was one of their star performers as they surged to their first French title for 17 years and to the latter stages of the French Cup, the French League Cup and the Uefa Champions League.
He is City's fifth major signing of the summer and he will will join up with his new teammates during their tour of the United States.
"I am absolutely delighted to join Manchester City," Mendy told the club's website "They are one of the biggest clubs in Europe and with Pep Guardiola they have a coach who likes attacking football. I am sure that we will win many trophies in the coming years."
Mendy joined a day after the Real Madrid defender Danilo completed his move to Manchester City for around 30 million euros.
Mendy's former Monaco teammate Bernard Silva was recruited to the City project earlier this summer while defender Kyle Walker from Tottenham Hotspur and goalkeeper Ederson Moraes from Benfica, have been transferred for a combined sum of 167 million euros.
Guardiola has made full-backs his top transfer priority in the close season having released Pablo Zabaleta, Gael Clichy and Bacary Sagna.