Goodson, who ran for 501 yards and three touchdowns in three seasons with Carolina, became expendable after the team signed free agent running back Mike Tolbert earlier this month.
He was fourth on the depth chart behind Jonathan Stewart, DeAngelo Williams and Tolbert, so his departure did not come as a surprise.
"Being behind DeAngelo and Stewart for a couple of years has been difficult just wanting to play and being a competitor," Goodson said. "I wasn't looking to leave but anywhere that gave an opportunity, I'm definitely up for that."
The Raiders needed depth at running back after losing Michael Bush to Chicago in free agency. Starter Darren McFadden has been injury prone, missing 19 games in his four seasons and Taiwan Jones played sparingly as rookie and is seen as more of a change-of-pace back.
With only five draft picks and none until the end of the third round, new Raiders general manager Reggie McKenzie is trying to fill as many holes as he can on the roster through free agency and trades.
In three seasons with the Panthers, Goodson played in 28 games with three starts.
He rushed 125 times for 501 yards and three touchdowns and added 43 receptions for 329 yards. Goodson, 24, had three straight 100-yard rushing games and three touchdowns late in the 2010 season under former coach John Fox in 2010.
But he didn't have any carries last year under new coach Ron Rivera and caught one pass for 4 yards.
"I thought going in, with the way I performed I'd definitely get an opportunity to play," Goodson said. "Some things happened. I didn't get the opportunity I thought I should have. Then I got injured, and it really didn't go the way I wanted last year."
Goodson has outstanding speed but fumbling has been a problem. He put the ball on the ground six times in 2010, losing three. During last year's training camp Rivera made Goodson carry a football around with him during one practice after he fumbled in back-to-back preseason games.
The former fourth-round draft pick in 2009 can also returns kickoffs.
"We wanted to acquire another player to compete at the running back position," McKenzie said. "He can do a lot of things in our scheme on offense. He's very versatile, he has natural running skills, he's a great receiver out of the backfield, and he has kick-return ability. I'm anxious to see if he can put all that together here as a Raider."
The 6-foot-6, 315-pound Campbell is the latest player who was one of late owner Al Davis' favorites to be sent out of town.
Picked in the fourth round in 2010 because of his impressive combination of size and speed, Campbell rarely saw action in two years with Oakland. He played only four games last season and was sometimes on the inactive list for game days when injured players who did not play were active.
He shifted between guard and tackle but never looked comfortable at either spot.
"We think Bruce Campbell is a very young, talented offensive lineman who has all the physical qualities to play in this league," Panthers general manager Marty Hurney said. "It gives us some more depth at a position where we needed some."
The Panthers view him as a tackle.
The Panthers have Jordan Gross at the left tackle spot, but last year rookie Byron Bell was pressed into starting on the right side in place of Jeff Otah, a former first-round draft pick who has been plagued by knee and back problems the past three years.
Both Bell and Otah are under contract this year.
"Mike is a talented player who gave us three good years, but our depth at running back allowed us to make this move," Hurney said.
AP Sports Writer Josh Dubow in Oakland contributed to this report.