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.
Zola was attracted by the challenge of restoring Aberdeen’s fortunes after four consecutive bottom-six finishes in the Scottish Premier League.
He said: “I was interested straight away because Aberdeen are a very big club that are well known throughout Europe, not just Scotland.
“They are a massive club with a great history and I know they have a great fan base who are very passionate about the club.
“I know a few people in football who actually played for the club including Zander Diamond. Everyone I spoke to including Zander confirmed what I already knew, that made the decision quite easy.
“I came here because I can be part of something special if we can bring the some glory back to Aberdeen. It is a great challenge for me as a footballer, something I am really looking forward to.”
Zola added: “I was impressed with the manager when I met him and his vision for the club.
“He also understood exactly what stage of my career I am at and what I want to achieve. He is a good manager who does things the right way and does his homework. I am sure the players will buy into what he wants to do here. I am very much looking forward to working with him and I am sure he will get the best out of me.”