The Champions League holders have beaten Manchester United to the highly rated midfielder's signature for an agreed fee of €20 million
Pep Guardiola recently already stated that he was keen to lure the 22-year-old to the Allianz Arena and the deal has now been completed as Thiago has signed a contract with the Bavarians until the summer of 2017.
The Spain international initially appeared to be on his way to Manchester United in search of regular first team football, but the presence of former coach Guardiola at the Allianz Arena eventually prompted Thiago to Germany instead.
"Thiago was bought at the strong desire of our new coach Pep Guardiola," Bayern chief Karl-Heinz Rummenigge told his new club's official website.
"We are pleased that we succeeded in this big transfer. Thiago has just been starring in the Under-21 Euros. He is a fantastic player who will strengthen Bayern."
The figure that Barca will receive for Thiago is set to rise to €25m following a friendly match between the European giants, which will be played in the following four years.
Thiago will compete with the likes of Bastian Schweinsteiger, Luiz Gustavo and Javi Martinez for a central midfield berth and joins Mario Gotze and Jan Kirchhoff as a summer arrival to the Champions League, Bundesliga and DFB-Pokal holders.