Roach's agent, Josh Wright, confirmed the deal on Friday. Terms of the deal are unknown, but it's believed that the Raiders offered a multiyear deal worth between $3 million and $4 million per year.
"I'm really going to miss Chicago, just everything about it, from the city to my teammates," Roach said. "I had a great six years with the Bears, and I can't even begin to describe how many friends I made on that team.
"But this league is all about the next step. There's a lot of turnover in the NFL, so while on one hand, I'm very sad to leave Chicago, this is going to be a great opportunity for me in Oakland."
The Raiders flew Roach to Oakland on Wednesday for an official visit and presented the versatile linebacker with a strong offer late Thursday afternoon.
The Raiders began the free agency period this week with just four returning starters on defense. They lost two of their top performers in free agency when defensive tackle Desmond Bryant signed with Cincinnati and linebacker Philip Wheeler signed with Miami. Oakland also released defensive back Michael Huff.
A six-year veteran, Roach has started 59 career games, spending the majority of his career as Chicago's starting strongside linebacker. He is expected to play middle linebacker for the Raiders.
"Once I came out here to visit, I had a pretty good idea that things were going to move quickly," Roach said. "It really benefited me to spend two days out here and get to know people in the Raiders organization and the Raiders' front office. This is a great fit. They made me feel so comfortable, and I was thrilled to wrap up the deal late last night the way we did.
"It's going to be great to be a full-time middle linebacker. I really like the type of defense they run here [4-3 scheme]. I can't wait to get with the coaches and really learn the system. Can't wait for this opportunity to play in the middle full time."
Roach filled in for Brian Urlacher at middle linebacker during the final four games of last season and finished the season sixth on the team with 84 tackles, including a career-best 15-tackle outing during the club's Dec. 23 win over the Arizona Cardinals.
After starting 10 games last season at strongside linebacker, Roach made his first start for an injured Urlacher at Minnesota on Dec. 9 and contributed 10 tackles, including one for lost yardage.
With Urlacher's future with the Bears in limbo, the club could be thrust into a situation where it would have to replace two starters at linebacker. Bears general manager Phil Emery said on Thursday the club approached Urlacher about returning to the team, but negotiations between the sides remain ongoing.
Emery also admitted the Bears are strapped for salary-cap space, which increases the likelihood they could be forced to part with at least one of their starting linebackers. The Bears already lost free-agent reserve linebacker Geno Hayes on Wednesday to the Jacksonville Jaguars.
Signed as an undrafted free agent out of Northwestern in 2007 by the San Diego Chargers, Roach started his career on that team's practice squad before it activated him in late November.
Roach started nine games for the Bears on the strong side in 2009, and aside from 2010, the linebacker has been one of the key contributors on defense ever since.
Roach signed a two-year, $4.5 million deal with the Bears in 2011 and is coming off a 2012 campaign in which he earned $2.815 million.
"I woke up to just a ton of text messages on my phone from my former Bears teammates," Roach said. "They were all wishing me the best, wishing me good luck. And it reminded me how fortunate I was to play with those guys in Chicago."
Information from The Associated Press was used in this report.