Williams signed a two-year, $10 million contract with a player option for the second season, sources told ESPN.com's Marc Stein.
"Welcome back home Deron Williams, the newest member of the Dallas Mavericks family!" Mavs owner Mark Cuban wrote on his Cyber Dust messaging app.
"We are excited to have him and you should be too. Make sure to give him a Mavs welcome when you see him."
Williams, a native of the Dallas suburb The Colony, agreed to the deal with the Mavs after receiving a buyout from the final two seasons of his contract with the Brooklyn Nets.
Williams opted to sign a five-year, $99 million deal with the Nets in 2012, when the Mavs also recruited him.
Brooklyn would have owed Williams $43 million over the next two seasons, but he accepted a buyout of $27.5 million with payments to be spread over five seasons, sources said.
Williams, a three-time All-Star, will attempt to resuscitate his career in Dallas after injuries contributed to a disappointing end of his Brooklyn tenure.
He averaged 13.3 points and 6.6 assists per game last season, shooting only 38.7 percent from the floor. Williams has career averages of 17.0 points and 8.5 assists per game.
"I'm a longtime fan." Dallas coach Rick Carlisle told ESPN.com. "When this situation popped up, it was almost like it was too good to be true. He's a tremendous player, and he's coming home."