The 23-year-old underwent a medical this morning and has been handed the number eight shirt after agreeing a transfer worth 40 million euros.
A statement on Bayern's website, www.fcb.de, this evening read: "The Spanish international has terminated his contract with the Basque club...and signed a five-year contract with the record German champions until June 30, 2017."
Martinez has been linked with the Bundesliga club throughout the summer and is relieved the deal has finally been completed.
"I am very happy and looking forward to playing for a club with such a history," said the Spain international.
"I've had a very long wait but finally that wait is over.
"Bayern are one of the best teams in Europe and throughout the world. There are so many top players here who play fantastic football - that's a big motivation for me.
"And, of course I want to win the title."