Wheeler visited the Raiders on Thursday and agreed to the deal a day later.
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.
A hole was created there earlier this month when the Raiders released Kamerion Wimbley. Wheeler is not the pass rusher that Wimbley is but is considered to be a better run defender, which is a big need in Oakland.
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."
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.
"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 Associated Press contributed to this story.