Martinez became the most expensive transfer in the history of the Bundesliga when he joined from Athletic Bilbao for a contractually-binding fee of 40 million euros, and Bayern are now even more confident they will end the year with at least one title after going two years without winning anything.
"We are convinced about this player," said Bayern's director of sport Matthias Sammer at a press conference today.
"Bayern have excellent cover in all positions, but the coach thought that we still needed this kind of a player. He will do us good.
Whether Martinez will be thrown in at the deep end against Stuttgart "will be decided by the coach", according to Sammer, but the Spain international cannot wait to make his debut.
"I am relieved that I am finally able to be here," he said. "Now I am concentrating on this season and getting to know my team mates.
"I would like to thank everybody who have made this possible."
Bayern started the season with a 3-0 win at Greuther Furth and are already sitting at the top of the table.
They could lose that place before they are in action on Sunday. Mainz host Furth on Friday night and can move top with a win.
On Saturday, defending champions Borussia Dortmund travel to Nuremberg while Fortuna Dusseldorf, who started out life in the top flight with a 2-0 win at Augsburg last weekend, can continue their perfect start to the season against Borussia Monchengladbach.
Elsewhere, Schalke host Augsburg and Eintracht Frankfurt travel to Hoffenheim while Werder Bremen stage the first northern Germany derby of the season against Hamburg.
Friday's Bundesliga Fixtures
Saturday's Bundesliga Fixtures
Sunday's Bundesliga Fixtures
Wolfsburg vs Hannover
Bayern Munich vs Stuttgart