Golden State is bringing Weber from the NBA Development League's Sioux Falls Skyforce, seeking depth and youthfulness in the backcourt.
"I've watched some tape on him over the last month or so. Our scouts really like him. Very athletic and defensive-minded," Warriors coach Steve Kerr said about Weber after Saturday's practice.
Weber, who will wear the No. 2 jersey, is focused on bringing support to the Warriors' defense. "I just want to make it tough for the opposing point guards when I'm on the floor," Weber said.
Weber, the D-League Player of the Month for January, is averaging 16.5 points, 7.4 rebounds, 7.2 assists and 36 percent from 3-point range.
Warriors backup point guard Shaun Livingston has been sidelined the past two games with a lower-back strain, resulting in Kerr going with a committee of unconventional players at the position.
Varejao, who has made only 14 appearances this season, was the odd man out. If he clears waivers, he'll become an unrestricted free agent.
Sources told ESPN's Brian Windhorst that Varejao could be a target for a waiver claim, with a team below the salary floor being able to save roughly $1 million by taking him.
ESPN's Chris Haynes contributed to this report.