Zola, who has had previous spells at Oldham, Tranmere and Crewe, racked up 16 goals last season but leaves Albion after their unsuccessful League Two play-off campaign.
"I'm delighted to get Calvin on board as our third signing of the summer," Aberdeen manager Derek McInnes told the club's official website.
"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."
The 28-year-old, who began his professional career with Newcastle, becomes Aberdeen's third summer signing after former Dundee United midfielders Willo Flood and Barry Robson.
McInnes is also hoping to secure the signature of former Rangers winger Gregg Wylde.