ESPN NFL Insider Adam Schefter reported that the deal is worth $27.5 million.
Bowen was projected to be the starting defensive end for the Cowboys, but decided to test the open market after becoming an unrestricted free agent.
"I think it's going to be a good fit," Bowen told ESPNDallas.com Thursday. "I wanted to stay in Dallas, they knew that, but it just didn't happen that way."
Last season, Bowen finished third on the team with 12 quarterback pressures and tied for fourth with four tackles for a loss. He moved into the starting lineup full time Nov. 14 at the New York Giants after Marcus Spears suffered an injury.
"I don't have any hard feelings toward Dallas," Bowen said. "We tried to reach a deal, but it wasn't what Washington was willing to offer."
The Redskins expect to have an opening on their defensive line, with sources telling Schefter that Albert Haynesworth was going to be traded to the Patriots.
The Cowboys entered free agency with three defensive ends -- Jason Hatcher, Spears and Bowen -- headed to the open market.
"It's all about business," outside linebacker DeMarcus Ware said of the three defensive ends. "You learn that from the CBA, those guys need to do what they need to do for their families, but I know they're ready to play football. I do talk to those guys, and they want to be Cowboys."
Calvin Watkins covers the Cowboys for ESPNDallas.com.