"In Europe, no team has more desire and chance to win the Champions League," said the Brazil winger, who sealed a season-long loan switch from the Allianz Arena last month, in an interview with Gazzetta dello Sport .
"I've noticed a lot of quality in the squad, I'll add my creativity.
"[I chose Juventus] because in three years they have played in two finals in Europe. This is a team that wants more and more chances to win the Champions League.
"I want to get into the history of this club. One year from the World Cup, I could not have chosen better company.
"I'm here to win everything, including the Champions League."
Having initially impressed at Bayern under Pep Guardiola, Costa found first-team opportunities harder to come by with Carlo Ancelotti in charge last season.
The 26-year-old maintains there was no problem in his relationship with Ancelotti and says he did not want to create the impression of taking an easy route out by seeking a reunion with Guardiola at Manchester City.
"After so many years, I wanted to avoid people thinking that I was playing just because he [Guardiola] was on the bench," Costa said.
"I also wanted Juve to make new experiences, to grow and learn another kind of football.
"Allegri is a coach who speaks a lot. He knows my potential and I feel I have confidence. I have positive feelings, I think I can do a lot with this team and with this coach."
On Ancelotti, he added: "I think he had little time to see me, between summoning to the national team and injuries. I did not prepare with him as I did with Guardiola but I also had good relations with Ancelotti. We were friends."