The 28-year-old has put pen to paper on a two-year contract with the SPL club after deciding to leave the Brewers following their unsuccessful 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 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."