Croatia international Mandzukic was Bayern's top Bundesliga scorer last season, finding the net 18 times as Pep Guardiola's men cruised to the defence of their title.
Despite that return, Mandzukic had been heavily linked with a move away from the Allianz Arena ever since Bayern announced the signing of Borussia Dortmund striker Robert Lewandowski.
The likes of Arsenal and Milan were reported to be interested in the 28-year-old's services, but more recently Atletico emerged as favourites for his signature.
And, speaking at Lewandowski's unveiling on Wednesday, Sammer confirmed Mandzukic looks set for a switch to the Spanish champions.
"There is a verbal agreement between Bayern, Atletico and Mario Mandzukic," Sammer said.
"We want to thank Mario Mandzukic for his performances at Bayern and wish him all the best for the future."
Atletico boss Diego Simeone is in the hunt for a new striker as last season's top scorer Diego Costa is set to join Chelsea.
