Williams posted, "Made a very tough decision today..." with an attached link that opened onto a Nets team logo.
Multiple media reports Tuesday put the three-time all-star's new contract at $98 million over five years. He was also being pursued by the Dallas Mavericks.
The news came as the Nets -- preparing for their first season in their new home at Brooklyn's Barclays Center -- are reported to have acquired all-star guard Joe Johnson from the Atlanta Hawks while also re-signing Gerald Wallace.
The 28-year-old Williams came to the Nets in a February 2011 trade with the Utah Jazz. He has averaged 17.6 points and 9.2 assists over 506 career games.