Wheeler played 13 games for Indianapolis last season, making 80 tackles and recording one sack. He played four seasons overall with the Colts with 182 tackles and two sacks.
"We're excited to add another veteran to complement our talented linebacking group," general manager Reggie McKenzie said. "He gives us a lot of athleticism and versatility. He's a player that can do a lot of things."
McKenzie said earlier in the week that strongside linebacker was one of the final starting positions that needed to be filled this offseason.
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.
"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."
He rushed 125 times for 501 yards and three touchdowns and added 43 receptions for 329 yards. Goodson 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.
"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."
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 return kickoffs and play all on all special teams units.
AP Sports Writer Steve Reed in Charlotte, N.C., contributed to this report