The 22 year old, who was previously linked with Manchester United, has now joined up again with his former Barca manager Pep Guardiola who took over at the Allianz Arena this summer.
He has agreed a four-year contract and moves for an initial fee of €20 million euros (Dh96m), with add-ons taking the total amount to €25m.
"FC Bayern Munich and FC Barcelona have agreed terms for the transfer of 22-year-old Thiago Alcantara," a statement on Bayern's website confirmed.
"In the course of the next few days, the Spain midfielder will travel to Munich for the obligatory medical before signing a four-year contract binding him to Germany's biggest club until 30 June 2017.
"The clubs have agreed a transfer fee totalling €25m. FC Bayern will directly pay €20m. The remainder will be financed by the proceeds of a friendly match agreed between the clubs. A further proportion of the remaining sum will be indirectly covered by Thiago Alcantara himself, as the player will forego part of his remuneration."
"Thiago Alcantara was the biggest wish of our new coach Pep Guardiola," said Karl-Heinz Rummenigge, the Bayern chairman. "We're delighted we've successfully negotiated this major transfer.
"Only recently, Thiago was named best player at the Under 21 European Championship. He's a fantastic player with huge potential, and he will make FC Bayern stronger."
Thiago scored a hat-trick in the final against Italy as Spain's youngsters won this summer's tournament in Israel.
He becomes the fourth member of that victorious squad to make a big-money move this summer, following Real Madrid's signings of Isco, Asier Illarramendi and Dani Carvajal.
Confirmation of Thiago's move will come as a setback to David Moyes, the new United manager, who has now been linked with a bid for another Barca midfielder in Cesc Fabregas.
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