Varejao suffered the injury in the Cavs' 125-104 victory over the Minnesota Timberwolves on Tuesday.
The procedure, on Varejao's left Achilles, was undertaken by Dr Brian Donley at the Cleveland Clinic, and the Cavaliers declared the surgery "successful".
The Cavs also confirmed the Brazilian's season was over.
"Varejao is expected to miss the remainder of the 2014-15 NBA season while he recovers and progresses through his rehabilitation process," part of a Cavs statement read.
"A timeline for his return to basketball activity will be established at a later date."
Tristan Thompson replaced Varejao at centre in the Cavs' only match since, their loss at Miami Heat on Christmas Day.
Varejao only signed a $30million, three-year contract extension with Cleveland in October, as he entered the final year of his original six-year deal.
The 32-year-old finishes the 2014-15 season with an average of 9.8 points and 6.5 rebounds per game.