The La Liga champions have agreed a deal with the Bundesliga holders to sign the Croatia international, who had been previously linked with Arsenal and Chelsea.
Gunners boss Arsene Wenger was thought to be a keen admirer of the giant striker, who scored 18 goals and made four assists in 30 Bundesliga appearances last season.
However, Atletico have won the race to sign the 28-year-old forward as Diego Simeone prepares for the departure of Diego Costa to the west London side.
“There is a verbal agreement between FC Bayern, Atletico Madrid and Mario Mandzukic,” A Bayern statement read.
“We want to thank Mario Mandzukic for his performances at FC Bayern and wish him all the best for the future.”
Mandzukic scored 33 goals in 54 Bundesliga appearances after joining Bayern from Wolfsburg in 2012.
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