Blind and Ajax severed ties in late December, with his contract at the Johan Cruyff Arena still having six months to run.
The 32-year-old was in his second spell at the club, with his two stints either side of a four-year spell at Manchester United, producing seven Eredivisie titles.
Blind made 19 appearances across all competitions in the first half of this season and played all five matches as Netherlands reached the Qatar 2022 FIFA World Cup quarterfinal stage, losing to Argentina.
Blind has signed a six-month contract at the Allianz Arena to continue his career in Germany.
"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," Blind told the official Bayern website.
"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."
Bayern sporting director Hasan Salihamidzic added: "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."
Blind is one appearance away from reaching 100 caps for the Netherlands national team.
