Sanches starred for Portugal during their Euro 2016 triumph last summer, before joining Bayern in a big-money move from Benfica, rejecting the chance to join Manchester United in the process.
The 20-year-old failed to score in 25 appearances for the German giants last season, however, and has been strongly linked with a move away from the Allianz Arena throughout this summer's transfer window.
Liverpool were reportedly in the race for the midfielder, but talk of Swansea's interest gathered pace earlier this week due to the presence of former Bayern assistant manager Paul Clement at the Welsh club.
Swansea, via an official statement, have now revealed that Sanches has joined the club on loan for the remainder of the season.
The highly-rated midfielder will join up with his new teammates after the international break.