The Raiders then used that pick to select University of Cincinnati cornerback John Bowie.
Moss, 30, has 101 touchdown catches to rank fifth in that category on the NFL's all-time list. In nine seasons, he has 676 receptions for 10,700 yards.
But last season, Moss scored only three times on 42 catches for 553 yards.
Rumors during the last day of the draft had Oakland deeming Moss expendable after acquiring receiver Mike Williams in a trade Saturday with Detroit.
"We felt this was the best scenario for both the Raiders and Randy," said new Oakland Coach Lane Kiffin.
Moss is the only player in league history to record 1,000 or more receiving yards in each of his first six NFL seasons, all with Minnesota.
If he returns to his old form, he would give Tom Brady the explosive wide-out the Patriots lacked in 2006.