The Athletic Bilbao midfielder has long been linked with a move away from San Mames, and will become the most expensive signing in the history of the Bundesliga.
The Spain international has long been linked with a move to the Allianz Arena, with the Bavarians looking to bolster their midfield options ahead of the start of the new season.
The transfer was triggered after Bayern activated a 40 million euro buy-out clause in Martinez's contract, despite Die Roten apparently being reluctant to meet the fee - a German transfer record.
It appears that Martinez was keen on the move being finalized however, as under the terms of the deal he will allegedly give up two million euros of his annual salary.
The versatile 23 year-old, who can play either as a central midfielder or defender, will sign a five-year contract, meaning he stands to lose 10 million euros overall.
Bayern has already added Claudio Pizarro, Mario Mandzukic and Xherdan Shaqiri to its ranks this summer, as it looks to wrestle the Bundesliga title from Borussia Dortmund.
Bayern was also hoping to sign Bayer Leverkusen midfieler Lars Bender during the summer transfer window, only for both player and club to rebuff its advances.