Martinez, 23, had rescinded his contract with Bilbao - which had a buyout clause of 40 million euros - and been given permission to join Bayern by the Spanish football federation (RFEF) and the professional football league (LFP), Bayern said in a statement on their website.
He has passed a medical and was available to play immediately.
"This was without question a complicated transfer so we are all the happier that Javi Martinez is finally with us," Bayern CEO Karl-Heinz Rummenigge said of the negotiations which have dragged on for several weeks.
Before Bayern confirmed the deal, Bilbao said in a statement that Martinez had travelled to Germany without their permission on Tuesday to finalise the move and they had asked him for an explanation.
Raised at Osasuna, Martinez was signed by Bilbao as a 17-year-old in 2006 and has played for Spain at all age levels. He flourished last season under coach Marcelo Bielsa, helping his team reach the finals of the King's Cup and the Europa League.
BOTH COMPETITIONS
Bayern are desperate to win a title this season after finishing as runners-up in the Bundesliga and German Cup last term, beaten by Borussia Dortmund in both competitions.
Bayern, also runners-up in last season's Champions League, have insisted that they can afford the versatile Martinez who can play either in central defence or in midfield.
The Bavarians, who set the previous record of 35 million euros when they signed striker Mario Gomez from VfB Stuttgart three years ago, are proud of their reputation as a club with solid finances who live within their means.
However, a series of nagging injuries to playmaker Bastian Schweinsteiger has prompted them to look for other options in the centre of midfield.
"He's a type of player we don't have at the moment," said sporting director Matthias Sammer this month, while club president Uli Hoeness had that the deal that it would not break the bank.
"Bayern have ambitious targets and we can afford it," he said. "We've worked for decades so that we don't have to go to the credit department for a transfer like this."
Although Martinez was in the Spain squad which won the 2010 World Cup and Euro 2012, he has only won eight caps and many are baffled as to why Bayern have forked out so much for a player who is not a regular international.
Former Bayern coach Ottmar Hitzfeld, now in charge of the Switzerland national team, has suggested that the expectation could weigh heavily on Martinez.
Bayern also announced that the Spaniard would be given the number eight shirt once worn by West Germany international Paul Breitner. His contract is for five years.
Bilbao had made it clear they wanted to hold on to both the Martinez and his Spain team mate Fernando Llorente, who has said he wants to leave and has been linked in media reports with a move to Italian champions Juventus.
The uncertainty over the pair's future has disrupted the Basque club's start to the season and they are b
