Yahoo! Sports' Adrian Wojnarowski first reported the trade, which will send New Jersey's 2011 first-round pick and the Nets' 1-7 protected 2012 first-round selection previously owned by Golden State to Utah.
Messages left for Jazz general manager Kevin O'Connor, president Randy Rigby and coach Tyrone Corbin have not been returned.
The unexpected trade of Williams follows the Feb. 11 resignation of longtime former Utah coach Jerry Sloan and assistant Phil Johnson.
Williams has often been frustrated this season, taking issue with everything from Sloan to a change-filled Jazz offseason that saw Utah lose Carlos Boozer, Wesley Matthews and Kyle Korver to free agency.
Williams was under contract with the Jazz through the 2011-12 season and held a player option for 2012-13. He recently shot down a report that he was interested in playing for the New York Knicks. But the two-time All-Star guard acknowledged that luring top-tier free agents to Salt Lake City was not easy.
Harris, 27, is averaging 15.0 points, 7.6 assists and 2.4 rebounds with the Nets. The 6-foot-3, 190-pound point guard is in his seventh season in the league.
Favors, 19, is averaging 6.3 points and 5.3 rebounds. The 6-foot-10, 246-pound rookie power forward was selected by New Jersey with the No. 3 overall pick in the 2010 NBA Draft out of Georgia Tech.
Harris and Favors had been linked to numerous teams in trade rumors during recent months.
Utah explored trading Williams last month, gauging his market value while the relationship between him and Sloan deteriorated.
Sources close to Williams had no idea the trade was about to finalized when contacted this morning, expressing shock and disbelief when asked about the move.
Brian T. Smith