The club reached a verbal agreement with Atlético on Wednesday, the fee reported to be €22 million. The announcement of Mandžukić's transfer came just hours after the club unveiled Robert Lewandowski, giving him Mandžukić's number 9.
The Atletico Madrid official website has also announced that Mandžukić has signed a four-year deal.
"We thank Mario Mandžukić for two great years here in Munich," said executive board member Jan-Christian Dressen. "We achieved seven titles with Mario in that time and his goals were often decisive for those. We wish him all the best not just athletically, but personally at his new club.
In Mandžukić's two seasons at Bayern, he scored 48 goals and registered 14 assists in 88 appearances. With his move to Atético Madrid, he now will play in the third different domestic league after spending four years in the Bundesliga.
If the €22 million fee is in fact true, it would be the second most Bayern have ever received for a transfer, the highest being the €25 million Manchester United paid for Owen Hargreaves. Bayern paid €13 million two years ago to acquire Mandzukic from VfL Wolfsburg.
Mandžukić will likely replace Diego Costa in the Atlético XI after the Spaniard's move to Chelsea.