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The Netherlands defender had been heavily linked with Royal Antwerp, but he jumped at the chance to join Bundesliga leader Bayern.
Blind has committed to a six-month contract, with the 32-year-old adding the Bavarian giant to his illustrious list of clubs, having also had a four-year stint at Manchester United that ended in 2018.
"We're delighted that Daley is joining our team. Daley is a versatile defender, capable of playing on the left or in the centre. He has great international experience and leadership qualities. I'm sure he'll help us," sporting director Hasan Salihamidzic said.
Blind travelled to Germany on Friday before undergoing a medical with Bayern. He has an implantable cardioverter-defibrillator, a device similar to a pacemaker, after being diagnosed in December 2019 with a heart condition.
That proved no obstacle to him signing, with Blind now set to feature as Julian Nagelsmann's side chase domestic and European honours.
Speaking on his transfer, Blind confirmed fighting for such trophies was a key factor in his decision: "I can hardly wait to play here. We’ve got the most important part of the season coming up, where it’s about titles – and a club like Bayern can win every trophy.
"The hunger for titles here at the club was key in my decision. I hope I can bring my experience to help the team. I’ll give everything for Bayern Munich."
With a four-point cushion over Freiburg, they lead the way in the Bundesliga after 15 games, while in the Champions League they face a testing last-16 clash against Paris Saint-Germain.
Blind scored for the Netherlands during their World Cup campaign in Qatar, netting in the 3-1 win over the United States at the last-16 stage.
He has 99 caps for his country and will be looking to complete a century in the early stages of Ronald Koeman's second spell in charge.
Across two spells at Ajax, he made over 300 appearances and won the Eredivisie on seven occasions – only Johan Cruyff and Sjaak Swart won more league titles with the Amsterdam giants with eight apiece.
He was formally released by the Dutch champions on December 27, with Ajax chief executive Edwin van der Sar saying at the time: "I hope he can find another club to end his successful career with."