The 38-year-old hasn't suited up in an NBA game since the 2016-17 campaign.
Varejao is familiar with the Cavaliers, having played 12 of his 13 NBA seasons in Cleveland.
After a brief stint with the Golden State Warriors, Varejao left the NBA in 2017 and signed with Brazilian club Flamengo while also continuing to suit up for the Brazilian National Team in FIBA events.
Varejao brings a veteran presence to a young Cavs team fighting for their playoff lives. Cleveland is seven games out of the final play-in round spot, with only 10 games remaining on its schedule.