The Dutchman has joined the Balearic Island club on a three-year deal for an undisclosed fee.
Zuiverloon moved to West Brom from Heerenveen for £3.2million in July 2008 and impressed initially before struggling to hold down a place in the starting XI last season.
The 24-year-old was pleased to have been given the chance to relaunch his career in the Primera Division.
"I hope to become a better player and help the team. I will do everything possible to help the team have a good season."