The trade announced Wednesday sends Moss to the team with which he started his NFL career in 1998. He spent seven seasons with Minnesota before going to the Oakland Raiders for two years. He'd been with New England since the 2008 season.
The teams didn't disclose what draft choice the Patriots would receive.
Moss, 33, is a seven-time Pro Bowl selection, including last season when he caught 83 passes for 1,264 yards and 13 touchdowns. This season he caught four passes, three of which ended up as touchdowns, but didn't have any receptions in Monday's win at Miami.
Over his career, Moss has 935 receptions for 14,604 yards and 151 touchdowns.
The career touchdown total is second in NFL history to the 197 caught by Jerry Rice. Moss had 23 touchdown receptions in 2007, his first year in New England, which is a league record.
"We feel very good about the opportunity to add a player of Randy Moss' caliber to this football team," said Vikings Coach Brad Childress. "He is a tremendous competitor and was an integral member of the Vikings organization from 1998-2004 ... I know the entire organization is thrilled to welcome him back to the Twin Cities and look forward to his contributions."