With speculation swirling around coach Pep Guardiola and his potential move to the Premier League at the end of the season, the contract extensions were a signal of strength for Bayern.
Versatile forward Mueller, whose previous contract ran out in 2019, was a top target for almost every major European club for the past seasons.
Spain international Martinez, who joined in 2012, signed an extension of his 2017 deal with 34-year-old fellow countryman Alonso, in his second season in Munich, extending by a year.
"We are delighted to have signed long-term deals with these important players," club CEO Karl-Heinz Rummenigge said in a statement.
"Thomas, Jerome and Javi know how to win titles and the Champions League as well. With them the team maintains its quality and stability in the long term."
Guardiola, whose own three-year deal runs out at the end of the season has kept quiet about his future with the club eager to extend the former Barcelona coach's contract.
The Spaniard refused to comment on the speculation and said a decision would be taken after the start of the winter break following Saturday's Bundesliga match against Hanover 96.
"Rummenigge and I have said that we will talk after the game. He knows everything and we talk often," Guardiola told reporters when asked about a decision."
Bayern have said they will announce a decision before the end of the year.
The Bavarians, who have won consecutive league titles under Guardiola, are five points clear at the top of the Bundesliga and through to the Champions League knockout stage.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
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