The Spanish champions have acted quickly to bring the 28-year-old target man on board after Spain forward Diego Costa sealed a move to English Premier League club Chelsea last week.
Mandzukic had become surplus to requirements at Bayern following the arrival of forward Robert Lewandowski from Bundesliga rivals Borussia Dortmund.
"The incorporation of Mario Mandzukic is great news because he has the features we were looking for to cover this position," Atletico sports director Jose Luis Perez Caminero said on the club website.
"He’s a winner, a player used to winning titles. He’ll contribute very much."
Mandzukic spent two years with the German champions, scoring 33 goals in 54 Bundesliga appearances. He netted the opener against Dortmund in the 2013 Champions League final, which Bayern won 2-1.
The striker has scored 15 goals in 52 appearances for Croatia, including two at the World Cup in Brazil where his team were eliminated in the group stages.
Atletico won their first La Liga title in 18 years and reached the final of the Champions League last season.
(Writing by Toby Davis in London; editing by Alan Baldwin)
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