A red-and-white Bayern scarf was painted above the cockpit of the jumbo Airbus 380 plane under the words, "Congratulations" as it landed with a delay.
Outgoing coach Jupp Heynckes and captain Philipp Lahm took the cup down the stairs from the plane onto a red carpet before being driven away from the airport in the team bus.
A few dozen airport and airline workers welcomed the team back. Bayern still has to play the German Cup final on Saturday and the club did not want a big ceremony. The team had a party at its London hotel after winning Saturday's final 2-1.
The plane parked at an isolated spot, out of sight of fans.
Overnight, about 150,000 fans celebrated the team's fifth Champions League title in a street party.
Bayern won the Bundesliga championship and can complete a unique treble for a German team if it beats Stuttgart in the German Cup final at Berlin's Olympic stadium on Saturday.
It will be the last match for Heynckes as coach of Bayern. He will be replaced in June by former Barcelona coach Pep Guardiola.