The versatile attacker made 51 appearances in all competitions under Pep Guardiola last season but was often overlooked for a starting role, with the news coming less than a week after requesting talks over his future.
New United manager Louis van Gaal has been linked with Muller, having handed the attacker his die Roten debut, but the Germany international has extended his contract by two further years.
"I had good talks with the club's representatives who made it clear to me I'm at the right spot here," he told the club's official website.
"I feel I'm an important part of the club's plannings. Since the year 2000 FC Bayern Munich are my club and will be in the next years."
Bayern captain Phillip Lahm has also penned new terms, with his new deal now running until 2018, and is looking forward to ending his career at the Allianz Arena.
"That's definitely my last contract. I'll end my career at FC Bayern. That was always my wish - I am very glad and happy," he said.
Chief executive Karl-Heinz Rummenigge also expressed his delight at the homegrown duo's decisions to stay put.
"Philipp Lahm and Thomas Muller are very important building blocks of FC Bayern," he said.
"Both have remained loyal to the club since the start of their careers and will play a major role in the future. We are very happy that both players have chosen the long term for Bayern Munich."