Silva, who becomes Pep Guardiola's first summer signing, will take the number 20 shirt and will be formally unveiled as a City player on July 1 on a five-year deal.
City are expected to spend big during this transfer window after clearing out a number of players who were out of contract.
Silva has impressed for Monaco this season helping them win Ligue 1 and reach the Champions League semi-final, beating City on the way.
And he admits the lure of working with Pep Guardiola convinced him to join.
“It feels great. To be honest I’m now at one of the best teams in the world. To be part of this club and to have this opportunity is great,” he said.
"I’m very happy to be part of Manchester City’s team and I look forward to trying to do my best to help the team reach their goals.
Pep Guardiola has secured his first signing of the summer with Bernardo Silva
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“If not the best coach in the world, he is one of the best.
"Of course when you have the opportunity of being trained by Guardiola, you don’t say no.
"As we all know, what he did in Barcelona and Bayern Munich was amazing and we expect also here that he will win titles. It’s great to be working with him and to have this opportunity.”
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Silva was also wanted by Manchester United and Barcelona but City stole a march on their rivals by agreeing a deal with Monaco this week.
The confirmation comes just a day after a number of players were released from their contracts including Jesus Navas, Willy Caballero, Pablo Zabaleta and Gael Clichy.
The creative midfielder, 22, made 51 appearances last season, scoring 10 goals and making a further 10 assists.
Silva has 12 Portugal caps and joined Monaco from Benfica in 2015.
In handing him the number 20 shirt City have hinted that Eliaquim Mangala does not have a future at the club.
Bernardo Silva joins Manchester City on a five-year deal
Mangala was always expected to depart after being loaned out to Valencia.
Joe Hart and Samir Nasri were both sent out on loan as well and their future look elsewhere.
Guardiola is also looking at a deal to bring in left-back Bernard Mendy from Monaco, as he looks for a vast improvement on his opening campaign in England.
City’s third-place finish was the lowest of Guardiola’s glittering coaching career, and he pinpointed a failure in both penalty areas as the reason for their underperformance.
The Blues boss wants his team to be more ruthless in front of goal, and hopes his new signing’s creativity will unlock Premier League defences next season.
He is also looking to shore up a defence that conceded 39 league goals during the campaign – six more than champions Chelsea and 13 more than runners-up Tottenham.
Tottenham’s Kyle Walker is Guardiola’s top target in the right-back role, while the City boss is also considering a move for Juventus centre-back Leonardo Bonucci.
Argentina international Zabaleta completed a free transfer move to West Ham yesterday, having announced just under two weeks ago that he would be leaving City after nine years.
Zabaleta said: “Sometimes a new challenge is all you need as a person and as a player. For me, after being in this country for so long, this is a new challenge for me in the Premier League and I’m ready for it and looking forward to it.”