The 30-year-old makes the move for an undisclosed fee after passing a medical in the Spanish city yesterday.
"I hope that I can settle into the team as quickly as possible," said Demichelis upon arrival in Malaga.
There, the defender reacquaints himself with Manuel Pellegrini, who was his coach at River Plate before he moved to Bayern in 2003.
"We have a great reciprocal faith," added Demichelis on the Bayern website.
Demichelis made a total of 173 appearances in the Bundesliga, scoring 13 goals.