The 28-year-old has long been linked with the club and had spoken of his desire to make the move as speculation swirled.
Confirmation of the signing has come after Sevilla said earlier this week they had agreed a deal to sell Jesus Navas to City, although the Barclays Premier League club - still without a manager as they wait to confirm the arrival of Manuel Pellegrini - are yet to announce a deal for the Spain winger.
City have not revealed the fee paid for Fernandinho but reports this week suggested he could cost in the region of £34million.
It would therefore appear a compromise may have been agreed with the Ukrainian club as there had been reports suggesting the release clause in the player's contract was £42.5million.
Fernandinho told the club's website, www.mcfc.co.uk: "This is a change, a challenge and a chance that I have been waiting a long time for.
"Playing in the Premier League for City is like a dream.
"My ambition here is to win all the titles, the team here is strong, and so is the greatness of the club and the supporters.
"Professionally this is a spectacular thing. Playing for a huge club in a huge league makes me so happy.
"I hope I will be able to repay City for what they have done for me.
"I know I will face challenges but I am prepared for them. Every player at a high level faces pressure and must respond and I am ready for that too.
"I know a lot about City. Ever since they expressed an interest in me, I have been learning more."
The signing is a decisive early blow for City in the transfer market after the frustrations of last summer.
Former manager Roberto Mancini regularly cited the failure to land major targets last year as one of the reasons for the team's regression this past season.
There has been a regime change since then with player recruitment now being driven by new director of football Txiki Begiristain.
Pellegrini, whose appointment is expected to be ratified in the coming days, will be expected to work under the philosophy of the club's hierarchy.
Fernandinho was tipped for stardom after scoring the winner for Brazil in the final of the 2003 World Youth Championship.
He is a deep-lying playmaker who has been playing for Shakhtar since a £7million move in 2005.
He has helped the club to six Ukrainian league titles as well as UEFA Cup success in 2009.
He is thought to have been on City's radar for some time and he shone in front of an English audience when playing against Chelsea in the Champions League last season.
Navas is expected to join him at the Etihad Stadium after Sevilla revealed his transfer has been agreed subject to a medical.
City have given no indication when this may take place but the 27-year-old is currently on international duty with Spain ahead of the Confederations Cup in Brazil.