The 22-year-old midfielder, who won the Confederations Cup with Germany last year and is set to be part of their World Cup squad in June, is considered among the finest talents in Germany.
"We are delighted that Leon Goretzka, a Germany international with great prospects, decided for Bayern Munich despite competition from big-name clubs from abroad," Bayern CEO Karl-Heinz Rummenigge said in a club statement.
"This means Leon Goretzka will remain in the Bundesliga."
The versatile player is out of contract with Schalke at the end of the season and will be a free transfer.
"Leon Goretzka informed us at the start of this week that he wanted to leave the club and join Bayern," Schalke sports director Christian Heidel told reporters.
Heidel said the player had passed a medical at Bayern on Thursday and Rummenigge had called to let Schalke know.
"We are losing a very, very good player," Heidel said.
Heidel said the club had tried everything to keep the player, who has risen to become leader in the team after joining as a teenager five years ago.
Bayern are 13 points clear at the top of the table and are on course for a record-extending sixth straight Bundesliga title.
(Reporting by Karolos Grohmann; Editing by Toby Davis)
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