The 26-year-old Brazil international has arrived at Juventus on-loan from Bayern Munich and is targeting glory in Europe.
“In three years it has played two finals in Europe, it is the team who has more and more chances to win the Champions League,” said Costa.
“I want to enter the history of this club. One year from the World Cup I could not have chosen a better team.
“I’m here to win everything, including the Champions League.”