Mandzukic, 28, scored two goals at the World Cup finals for Croatia but just prior to the tournament confirmed he would be leaving Bayern due to coach Pep Guardiola's tactics.
Now Bayern, who signed the striker from Wolfsburg in 2012, have agreed to sell him to reigning Liga champions Atleti.
"Still nothing has been signed, but there is a verbal agreement between both Bayern and Atletico Madrid as well as between Mario and Atletico," said sporting director Matthias Sammer on Wednesday.
Mandzukic will be Diego Costa's replacement at Atleti following the news that the Spain striker is joining Chelsea.
The Croatian attempts to live up to an impressive recent succession of strikers at Vicente Calderon, including Falcao, Sergio Aguero and Fernando Torres.
- Sports & Recreation
- Atletico Madrid
- Pep Guardiola