Williams, the top free agent available, chose to stay with the Nets over signing with his hometown team, the Dallas Mavericks.
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 Thursday. He met with both teams Monday, the day after free agency opened, and made his Twitter posting about 7 p.m.
The person confirmed the agreement on condition of anonymity because contracts can't be signed until July 11.
Williams' decision comes a day after Brooklyn agreed to a deal with Atlanta for all-star guard Joe Johnson, and amid reports the club was still hoping to make a deal with Orlando for Dwight Howard.
Thunder seal Brooks deal. Scott Brooks always believed he would be back as the coach of the Oklahoma City Thunder, even as his previous contract was surprisingly allowed to expire following the NBA Finals.
There were rumors that he would be replaced by 11-time NBA champion Phil Jackson or Jeff Van Gundy - which general manager Sam Presti discarded as "rubbish" - but Brooks remained confident.
"I knew it would work out," Brooks said at a news conference to formally announce the deal he signed Monday.
Brooks reportedly now has a four-year deal worth more than $4 million annually, but the team isn't releasing the terms.
Allen, Heat to talk. The Miami Heat will get to make their sales pitch to Ray Allen.
A person familiar with Allen's plans said the free-agent shooting guard would visit with Heat officials Thursday. Allen also is scheduled to visit Friday with the Los Angeles Clippers, according to the person who spoke on condition of anonymity because the plans were not announced.
Warriors sign Barnes. The Golden State Warriors signed first-round pick Harrison Barnes. Terms of the deal with the 20-year-old former North Carolina forward were not disclosed. The 6-foot-8 Barnes led the Tar Heels with 17.1 points per game last season.
Pacers ink Hill. The Indiana Pacers and point guard George Hill have agreed to a new deal. Hill's co-agent, Michael Whitaker, wrote in a text message that Hill, a 26-year-old restricted free agent, will sign once the NBA's moratorium period ends July 11. Whittaker did not disclose terms.
Fields Toronto-bound? Knicks guard Landry Fields could be on his way out of New York after agreeing to sign an offer sheet with the Toronto Raptors.
The Octagon agency confirmed the deal, reported by ESPN.com to be for three years and about $20 million.
Since Fields is a restricted free agent, the Knicks will have three days to match the offer after it can be signed on July 11.