The 22-year-old struggled to hold down a regular first-team spot at Eastlands since joining the club from Hamburg last summer and made just 16 appearances in the Premier League.
Boateng was in Los Angeles with Roberto Mancini's first-team squad but flew back to iron out the deal with the Bundesliga side.
The Berlin-born defender is being lined up to play at centre-back for Bayern and is believed to have penned a four-year contract.
Source: Team Talk
Source: Team Talk