The deal is worth a maximum value of $12 million, a league source told ESPN NFL Insider Adam Schefter.
"From the moment that I came here off my flight, just the fans here were unbelievable telling me how important it is to stay here in the Raider Nation," Woodley said. "I know a little bit about the history of the team, and once I started talking to the coaching staff and telling me how they were going to use me in the defense, I was excited and I was saying that this place is going to be the place for me."
The Steelers released Woodley earlier this week. He had been the highest-paid defensive player in team history.
Woodley played left outside linebacker in Pittsburgh's 3-4 alignment, but will switch to defensive end in the Raiders' base 4-3.
"I don't feel like it's any different than playing a 3-4 outside linebacker, where you are still kind of the defensive end," Woodley said. "The only thing about the 3-4 scheme is that you are asked to drop back and cover receivers and you are standing up rushing. You still have to play the run, you still have to get after the quarterback, and that's no different from a 4-3 end. So, your hand is in the dirt and you're not dropping back in coverage."
Woodley believes the Raiders aren't far off from turning things around.
"With a few pieces added to this team, this team can be a good team," he said. "When I played in Pittsburgh last year, we came out here to Oakland and we lost. So, I feel like Oakland has a good team. The past few years with the salary cap and the different things going on, Oakland wasn't in the situation, really, to go out and get free agents like they can get now, or even in the draft they weren't able to go out and draft a bunch of new guys because of the situation it was in. But, I think now coming this year, those situations have changed."
Oakland also reached a deal with ex-Giants defensive end Justin Tuck on Thursday.
"I feel like we bring leadership and experience to this defense," Woodley said. "Me and Justin both have played in two Super Bowls. He has won two, I've won one Super Bowl but we know what it's like to be on a winning team, and we know what it takes to get there."
Woodley, 29, was a productive pass-rusher during a four-year stretch from 2008 to '11, but struggled in recent years and lost his usual starting position of left outside linebacker to Jason Worilds, moving to the right side this past season for Pittsburgh. Woodley had just five sacks in 2013.
A second-round draft selection in 2007, Woodley has spent his entire career with the Steelers, recording 57 sacks.
The Raiders need help on their pass rush after losing last year's leading sacker and most consistent defender, Lamarr Houston, to Chicago in free agency. The other three starting defensive linemen -- Pat Sims, Vance Walker and Jason Hunter -- are also free agents.
Information from the ESPN.com Raiders reporter Paul Gutierrez and The Associated Press was used in this report.