The former Manchester United star agreed to terminate his deal with the Dutch giants last month, making him a free agent.
Blind had been expected to sign a short-term deal with Belgian side Antwerp, while Club Brugge were also interested.
However, Bayern have made a shock swoop for the veteran and now expect to sign Blind on an initial six-month deal.
The Dutchman is expected in Bavaria today to complete the first part of his medical and the deal will include the option of a further 12 months.
Blind had two stints at Ajax and he left the Amsterdam club for Manchester United in 2014 following Louis van Gaal’s appointment at Old Trafford.
He returned to the Dutch capital four years later and he made 333 appearances for his boyhood club.
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