Players paraded the German Cup, Bundesliga and Champions League trophies from a rain-protected open-top bus through Munich amid a sea of umbrellas sheltering jubilant fans.
The slow-moving parade made its way to Munich's town hall, where injured defender Holger Badstuber was first to appear on the balcony to a rousing reception from an estimated 10,000 people.
Bayern captain Philipp Lahm then presented the Bundesliga trophy once more, Bastian Schweinsteiger held up the German Cup and outgoing coach Jupp Heynckes hoisted the Champions League trophy.
"In 1990, I stood here on the balcony and rather rashly promised the European Cup," Heynckes said of his first stint at the club. "I'd like to deliver on that promise today. Here is the European Cup of national champions, the Champions League."
Heynckes, who is making way for former Barcelona coach Pep Guardiola, paid tribute to the Bayern supporters.
"We don't only have a world-class team, we have world-class fans," the 68-year-old coach said. "We'd never have achieved all this without such fans."
Police expected up to 100,000 fans celebrating around the city.
Bayern defeated Stuttgart 3-2 to win the German Cup final in Berlin on Saturday, one week after Heynckes' side won the Champions League and some eight weeks after securing the Bundesliga title.
Bayern became the first German club to win the treble of domestic league, cup and European Cup, and only the seventh overall.
"Bayern were really so strong this year that they deserved all three titles," Germany coach Joachim Loew said.
Police expected up to 100,000 fans celebrating around the city.Suggest a correction