Campbell, who started every game at quarterback for Washington in the past two seasons, became expendable when the Redskins earlier this month acquired former Philadelphia Eagles starter Donovan McNabb.
"I talked to (Raiders owner) Al Davis and he said he wants me there," Campbell told Oakland's website (www.raiders.com). "That means a lot to me. I'm ready to get to work."
Campbell, 28, compiled a 20-32 record as a Redskins starter. He threw for 55 touchdowns and 10,860 yards in five seasons with Washington.
"I'm just glad the situation is over and I'm moving forward," he told the Washington Post (www.washingtonpost.com). "Sometimes change comes in your life, change comes in your career, and you've just got to be ready to adapt."
(Reporting by Gene Cherry in Raleigh, North Carolina)