The 28-year-old has penned a two-year contract after deciding to leave Burton following their unsuccessful npower League Two play-off campaign.
Zola, who was born in the Democratic Republic of Congo, began his professional career with Newcastle but failed to make a first-team breakthrough.
The 6ft 3in forward went on to play for Oldham, Tranmere and Crewe before spending two and a half years at Burton, where he struck 16 goals last season.
Aberdeen manager Derek McInnes told the club's official website: "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."
McInnes previously signed former Dundee United midfielders Willo Flood and Barry Robson, and is also trying to secure the signing of former Rangers winger Gregg Wylde amid competition from the likes of Motherwell.