The Vikings sent a third-round pick to the Patriots in return for Moss, who becomes a key weapon for Minnesota QB Brett Favre.
The teams had not yet confirmed the trade. But Vikings S Madieu Williams said on Twitter that the deal was "official."
Moss returns to the team where he spent the first seven years of his career. Moss caught 574 passes for 9,142 yards and 90 TDs from 1998-2004 in Minnesota.
It leaves the Patriots and QB Tom Brady without the stretch-the-field wideout who set an NFL single-season record of 23 receiving TDs in 2007.
Moss did not get a contract extension from the Vikings as part of the deal, NFL Network reported.
ESPN reported that Patriots coach Bill Belichick spoke by phone to inform Moss of the trade on Wednesday morning. The network described their conversation as cordial.
For Favre, the trade gives him a serious receiving threat that he has long lobbied to acquire and that he has lacked this season with Sidney Rice injured. Favre, with the Packers in 2007, pushed the team to acquire Moss but lost out to the Patriots.
The receiver will return to New England on Oct. 31, when the Vikings visit Foxborough to the play Patriots (a game that occurs only once every eight years). Fox was already scheduled to broadcast that game nationally at 4:15 p.m. ET.
Moss' final game in a New England uniform on Monday turned out to be his only in more than three years in which he did not catch a pass. The Herald reported that Moss had asked the Patriots to trade him after Week 1, when he had an outburst about his contract following a win against Cincinnati. Moss later apologized and said he and coach Belichick had cleared the air.
Moss, whose deal expires after the season, said after Week 1 that he wanted to stay with Patriots but added he thought this would be his final year in New England.
Moss is set to appear on Monday Night Football for the second straight week when the Vikings travel to play the New York Jets next week. He'll likely be matched up again with Jets CB Darrelle Revis, who hasn't played since tweaking his hamstring on a TD pass he allowed to Moss in Week 2.
Moss will be just second player to appear on MNF back to back. Keith Browner played for the San Francisco 49ers against the New York Giants on Oct. 5, 1987, then played for the Los Angeles Raiders against the Denver Broncos on Oct. 12 (via ESPN and Elias Sports Bureau).
Since the Vikings have already had their bye and the Patriots' is Sunday, Moss could become the sixth player to play in 17 games if he plays in the rest of the Vikings' contests.
-- Sean Leahy