The striker had been linked with a move away from the Allianz Arena following Robert Lewandowski's arrival and Matthias Sammer has confirmed the wheels are in motion.
The Spanish champion was in the market for a new striker following the departure of Diego Costa to Chelsea and has now found its man in the Croatia international.
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The 28-year-old had joined Bayern from Wolfsburg in the summer of 2012 and was part of the team that won the treble in 2012-13, while also winning the domestic double last season.
Nevertheless, he was deemed surplus to requirements by head coach Pep Guardiola following the arrival of Robert Lewandowski from Borussia Dortmund and will now continue his career at Atletico once all formalities are completed.
"There's a verbal agreement between Atletico and Bayern and between Mario Mandzukic and Atletico," Sammer revealed at a press conference. "There's nothing signed yet but I think we can trust those words. We thank Mario Mandzukic and we will always remember the successes we have achieved together.
"He has always acted correctly and as a role model. I can only say positive things about him."
Mandzukic netted 33 goals in 54 Bundesliga appearances during his two seasons at the Allianz Arena.