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Silva's arrival, set for July 1, is the first high-profile signing by City manager Pep Guardiola ahead of the 2017/18 campaign.
City gave no indication of the length of Silva's contract nor did they specify a fee, although British media reports suggested they had paid around £43 million ($55 million, 49 million euros) for the 22-year-old.
Manchester United were also said to be interested in signing Silva but it was the Etihad Stadium club he opted for after flying into Manchester Airport on Thursday.
"It feels greatou have the opportunity of being trained by Guardiola, you don't say no. If not the best coach in the world, he is one of the best.
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"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," added Silva, capped 12 times by Portugal.
Silva started his career with Portuguese giants Benfica before moving to Monaco in 2014 on a season-long loan.
But so impressive was his start to life in French football, the deal was made permanent six months in.
Last season saw Silva score 10 goals in 51 appearances last season, and assist in the creation of a further 10, as Monaco won Ligue 1 and reached the semi-finals of the Champions League, having beaten Tottenham Hotspur, City and Germany's Borussia Dortmund en route.
"Muito Obrigado Bernardo... and Good Luck!," said Monaco on their website.
Spaniard Guardiola recently cleared out four senior players including winger Jesus Navas and defender Gael Clichy after the club finished a distant third behind Premier League champions Chelsea this term.
As well as Navas and Clichy, goalkeeper Willy Caballero and Bacary Sagna were also deemed surplus to requirements by Guardiola, with it having long been apparent that Pablo Zabaleta, who signed for English top-flight rivals West Ham on Friday, was on his way out.
Meanwhile the City future of midfielder Yaya Toure remains uncertain after he was initially sidelined by Guardiola, only to fight his way back into the reckoning for a first-team place.
The 34-year-old Ivory Coast international is also out of contract and it is not clear whether he would accept the likely pay cut needed to secure a short-term deal.
It leaves Guardiola looking to City's Middle East owners for money to spend on up to five new players as he tries to close the 15-point gap between his side and Chelsea, with the club also finishing eight point adrift of second-placed Tottenham.