The midfielder said at his official unveiling that he aims to adapt quickly to English football and prove his worth to Manuel Pellegrini, and Brazil coach Luiz Felipe Scolari
The 28-year-old sealed a 34.8 million euro move to the Premier League runners-up in early June, and was officially unveiled, alongside new manager Manuel Pellegrini, on Wednesday.
Fernandinho outlined his aim to adapt to English football and admitted the increased schedule will be a "challenge", but he is keen to show the club his worth by aiding Pellegrini in his search for silverware.
"In Ukraine, as well as in Brazil, City nowadays are seen as one of the best in the world," he told reporters. "After I signed for Man City the people back home in Brazil congratulated me for signing for one of the top teams.
"I think the main challenge for me is a different style of play compared with my last team and also the amount of games throughout the season.
"I want to repay the club for what they have done for me by playing well on the pitch and by winning as many trophies as possible, that is one of my aims.
"My relationship [with Shakhtar coach Mircea Lucescu] was fantastic and I hope to build the same relationship with Mr Pellegrini."
With the new season leading up to Brazil's hosting of the 2014 World Cup, and Fernandinho missing out on a place in the recent Confederations Cup success, the midfielder is hoping to impress Selecao coach Luiz Felipe Scolari.
He added: "My first aim is to play well for Manchester City, and if I have good performances I'm sure that will catch the attention of the national manager. But the first thing is to play well."
Fernandinho, who joined Shakhtar from Atletico Paranaense in 2005, has been capped just five times by his country.