The 28-year-old Brazilian midfielder was unveiled at the Etihad on Wednesday after completing a 34 million pound move from the Ukrainian champions
The 28-year-old leaves Ukraine after eight successful seasons with Shakhtar, having won the league on six occasions.
“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," the Brazilian international told the club's official website.
“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."
Fernandinho, a former Atletico Paranaense man, has five senior caps for Brazil, and caught the eye with the winning goal against Chelsea in October's Champions League victory.
He is expected to be joined by Sevilla winger Jesus Navas, who has agreed to move to Manchester in a deal worth around 20 million pounds following the completion of a medical.