Details of the terms were not disclosed but agent Dan Fegan told The Plain Dealer newspaper that the club and Varejao agreed on a six-year contract worth up to 50 million U.S. dollars.
Brazilian Varejao has played five years in the NBA, all with the Cavaliers.
Known for his hustle, Varejao posted career-highs with 42 starts and 8.6 points per game as the Cavaliers won a league-high 66 regular-season games but was eliminated in the Eastern Conference finals by Orlando.
The signing is the second major off season move by the Cavaliers, who completed a blockbuster trade on June 25 to acquire center Shaquille O'Neal from the Phoenix Suns.