City, who have yet to appoint a successor to sacked manager Roberto Mancini, did not give any financial details of the deal but British media have widely reported the transfer fee to be about 30 million pounds.
The pacy 28-year-old Fernandinho had been on City's radar for much of the season and is known in England for scoring in the Ukrainian club's 2-1 victory at home to Chelsea in the Champions League group stages last season.
"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," he told the club's 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."
Fernandinho, who has five Brazil caps, had previously said he hoped a move to City would improve his chances of making the national squad for the 2014 World Cup on home soil.
He started his career with Atletico Paranaense in his homeland before becoming one of a host of talented Brazilians to head for Shakhtar, with whom he has spent the last eight seasons and won the 2009 UEFA Cup.
Before his departure, Mancini had spoken of the need for the club to act faster than last season in the transfer market if they wanted to prise the Premier League crown back from arch-rivals Manchester United.
The Italian may have left but City, widely expected to name departing Malaga coach Manuel Pellegrini as the new boss, seem to have heeded Mancini's words as the signing comes days after Sevilla said their winger Jesus Navas was joining the club.
City gave up the Premier League title without much of a fight as United secured a 20th league trophy with four games to spare. City also lost the FA Cup final to Wigan Athletic, who were relegated from the top flight days later.
Mancini had laid some of the blame for their disappointing season on the failure to capture Netherlands striker Robin van Persie, who joined United in the close season and whose league-leading 26 goals drove their title charge.
