Bayern Munich have completed the long-expected transfer of the Chile midfielder Arturo Vidal from Juventus on Tuesday.

The Bundesliga champions said that Vidal signed a deal through to 2019 while Italian media reports suggested Bayern paid €36m (£25.5m), rising to €40m with bonuses, to bring the 28-year-old Vidal back to the Bundesliga.

“I’m very happy,” he told the club’s website. “This is a new step in my career and I hope I do well here. I want to help the team and win trophies. It’s a dream come true for me personally.

“I wanted to take another big step forward in my career. I want to keep developing as a player and win important trophies like the Champions League. I think the best opportunity to do so is with Bayern.”

Vidal scored 15 goals in 117 league games over four seasons for Bayer Leverkusen before leaving for Juventus in 2011 and the midfielder is expected to fill the gap left by the departure of Bastian Schweinsteiger for Manchester United, as well as to give Pep Guardiola’s team more toughness.

Vidal was brought to Germany at the age of 20 from the Chilean club Colo-Colo by then Leverkusen squad director, Michael Reschke. Reschke ended his 35-year association with Leverkusen when Bayern appointed him as a director in June.

Vidal helped Juventus to four consecutive Serie A titles and, last season, to the Coppa Italia. Barcelona denied the club a treble by winning the Champions League final between them in Berlin.

Vidal, capped 69 times by Chile, helped the team to their first Copa América win earlier this month scoring in the penalty shoot-out win over Argentina in the final. However, his tournament was overshadowed when he had his driving licence temporarily revoked by a Chilean judge for drink-driving.

He reached a deal with prosecutors to avoid trial after crashing his Ferrari and he apologised for insulting a police officer, as well as agreeing to pay compensation to a driver involved in the crash.

It was not the first time that Vidal had been involved in a controversial incident. In 2011, he was one of five Chile players handed a 10-game ban after breaking a curfew and returning to the country’s training base 45 minutes late.