The 28-year-old Congolese forward has scribed a two-year deal with the Dons.
Zola began his career with Newcastle United and also had spells with Oldham, Tranmere and Crewe before joining Burton in July 2011.
Manager Derek McInnes told RedWeb: "I'm delighted to get Calvin on board as our third signing of the summer.
"He has all the attributes which I think will be beneficial to the team and he will complement our forward players.
"He is at a good stage in his career, he's at a good age and when I spoke to him I felt he had a real enthusiasm to be part of something here at Aberdeen FC."
Zola scored twice in the League Two play-off semi-final first-leg victory at Bradford last month - see the goals below (despite SSN believing Calvin Harris scored them...)