Blind became a free agent last week after agreeing to terminate his contract with Ajax six months early.
"We are really pleased that Daley has joined the team," Bayern's sporting director Hasan Salihamidzic said.
"Daley is a versatile defender who can play on the left-hand side as well as in the centre. He has lots of international experience and leadership qualities."
Blind, who helped the Netherlands reach last year's World Cup quarter-finals in Qatar, won seven titles with Ajax, making 333 appearances, scoring 13 goals and contributing 21 assists.
He also won the 2017 Europa League during his spell with Premier League club Manchester United.
German champions Bayern, who top the Bundesliga standings, resume their campaign against RB Leipzig on January 20.RB Leipzig