Williams' buyout is complete with the Charlotte Hornets and he was waived Saturday. He will clear waivers Monday with the remainder of his $15 million expiring salary and become an unrestricted free agent.
Williams will sign with the Bucks on the veterans' prorated minimum worth $956,000, according to ESPN's Bobby Marks.
Buyout players are eligible for the postseason on their next team, as long as they've completed contract buyouts by March 1.
The Bucks, who at 44-7 have the best record in the NBA, did not make a trade before Thursday's deadline.
Williams' ability to defend multiple positions, shoot 3-pointers (36.2% in his career) and deliver character to a locker room makes him a coveted player on the buyout market.
Williams, 33, has played with Charlotte since 2014, and his career includes stops with Utah (2012-14) and Atlanta (2005-12). The 15-year veteran has averaged 25 minutes per game in 49 career playoff appearances, last reaching the postseason with Charlotte in 2016.
He was a starter for the Hornets until this season, when he has made just one start in 41 games played. He has career averages of 10.3 points, 5.2 rebounds and 1.3 assists in 1,055 games.
Bender, 22, has appeared in seven games for the Bucks this season and is averaging 3.7 points and 2.9 rebounds.
Williams is not the only player Charlotte is trying to buy out. Sources told ESPN the Hornets are finalizing a buyout of former No. 2 overall pick Michael Kidd-Gilchrist, with the small forward possibly headed to the Dallas Mavericks.