The striker is set to complete a switch to the Spanish champions, having been pushed down the pecking order at the Allianz Arena following Bayern Munich's signing of Robert Lewandowski.
Bayern's sporting director Matthias Sammer confirmed on Wednesday that terms had been agreed for the sale of Mandzukic.
The Croatia international is in line to replace Diego Costa - now a Chelsea player - and said Simeone was a key factor in him opting for Atletico.
"I am very happy to be here. I am well aware of Atletico and I know they have good players and a good coach," he told Marca.
"I know a lot about Atletico, I have seen several games and I like the style of play.
"The coach is very good, they have good players, and I think I can do great things with this team."
Mandzukic has won two Bundesliga titles, the UEFA Champions League and two DFB-Pokals with Bayern.
The former Wolfsburg man scored 25 goals in all competitions last season, but the arrival of Lewandowski looks to have signalled the end of his time with the German champions.
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