The All-Star point guard said on his Twitter page Tuesday night that he "made a very tough decision today" and posted a picture of the Nets' new team logo that accompanies their move from New Jersey to Brooklyn.
A person with knowledge of the decision said Williams told the team he was accepting their five-year contract worth $98 million. The person confirmed the agreement on condition of anonymity because contracts can't be signed until July 11.
Williams, the top free agent available, chose to stay with the Nets over signing with the Mavericks, who hoped they could convince him to come back to the area where he grew up.
It's a huge triumph for the Nets as they prepare to move into the new Barclays Center to start the 2012-13 season. They gave up an enormous package to get Williams in a surprising February 2011 trade, sending promising forward Derrick Favors, point guard Devin Harris, two first-round draft picks and cash to the Utah Jazz.
But it was worth it for the Nets, who needed a franchise player with them to build buzz for their move to New York.
Williams wanted to make a quick decision before he reports to training camp in Las Vegas with the U.S. men's basketball team on Thursday. He met with both teams Monday, the day after free agency opened, and made his Twitter posting at about 7 p.m. ET.
Williams' decision comes a day after the Nets agreed to a deal with Atlanta for All-Star guard Joe Johnson, and amid reports they are still hoping to make a deal with Orlando for Dwight Howard. Brooklyn also has a deal in place to re-sign versatile free agent forward Gerald Wallace.
Just two years after a 70-loss season, the Nets will have one of the NBA's best backcourts and are poised to make a quick move up the Eastern Conference standings.
Dirk Nowitzki and the Mavericks had spoken openly about their desire to bring Williams back to North Texas, where he starred at The Colony High School. Mark Cuban's team never made much attempt to defend its 2011 NBA title, letting key players such as Tyson Chandler and J.J. Barea leave through free agency so the Mavs could save money for this summer.
But Dallas could only offer Williams a four-year deal worth about $75 million under the terms of the new collective bargaining agreement. And with the Nets' flurry of moves, may not even be able to offer a better team anymore.
Williams averaged 21 points and 8.7 assists last season and had a 57-point game. One of the league's top point guards since entering the NBA as the No. 3 pick of the Jazz in 2005, he was ahead of his competitors when last season started after playing in Turkey during the lockout.
The Jazz decided to deal him at the 2011 deadline after a clash with former Utah coach Jerry Sloan, and without knowing if Williams would stay there long-term. The Nets had just been stung when the Knicks beat them to acquire Carmelo Anthony from Denver, and the Nets bounced back the next day by landing Williams.
Williams didn't always seem to enjoy playing in New Jersey, with the Nets spending the last two seasons in a temporary home in Newark. But he should play in front of packed crowds in Brooklyn as the main attraction at the Barclays Center.