The Warriors announced the move Friday.
According to Adrian Wojnarowski of The Vertical, the Dubs plan to sign Weber to a 10-day contract.
The 34-year-old Varejao has appeared in just 14 games this season and averaged 1.3 points and 1.9 rebounds per contest.
The Brazilian big man has posted 7.3 points and 7.2 rebounds per game in his career. He spent 12 seasons with the Cleveland Cavaliers before joining the Warriors in 2015-16.
The former VCU standout is averaging 16.5 points, 7.5 rebounds and 7.4 assists for the D-League's Sioux Falls Skyforce this season. He was named the D-League Player of the Month in January.
The 24-year-old will provide backcourt depth for a Warriors team that has been without guard Shaun Livingston for the past two games due to a back injury.