The Champions League holder beat Manchester United to the highly-rated midfielder's signature after triggering his buy-out clause
Pep Guardiola recently 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 FCB until the summer of 2018.
The Spain international initially appeared to be on his way to Manchester United in search of regular first team football, but the presence of Guardiola at Bayern eventually prompted Thiago to move to the Allianz Arena instead.
"Thiago was bought at the strong desire of our new coach Pep Guardiola," Bayern CEO Karl-Heinz Rummenigge is quoted as saying in Welt Am Sonntag.
"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 fee that Barca will receive for Thiago is set to rise to 25 million euros following a friendly match between the European giants, though no date has been confirmed as of yet for the clash.
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 Bundesliga champion.