The Dolphins will receive a second-round pick in 2009 and a sixth-rounder in 2010.
According to ESPN.com's John Clayton, Taylor told the Redskins he did not need to renegotiate and was willing to play for the final two years of his contract. He is scheduled to make $8.1 million this season. With around $9 million of cap room, the Redskins were able to work the trade quickly.
The Dolphins had been waiting for an opportunity to trade Taylor, who asked to be moved to a playoff contender at the beginning of the offseason. Before the draft, the Dolphins were asking for a first-round draft choice. They lowered the demand later to a second-rounder.
Taylor didn't exactly win over Miami executive vice president of football operations Bill Parcells. The veteran missed all of the team's offseason work while competing in ABC's "Dancing With The Stars."
A six-time Pro Bowl defensive end and the 2006 NFL Defensive Player of the Year, Taylor fell out of favor in Miami after spending his offseason on the TV show rather than working out with teammates.
"We're fortunate there was a guy that caliber on the market when somebody got hurt," Washington executive vice president Vinny Cerrato said. "Normally, in most years, there's not a guy of that caliber on the market."
The 33-year-old Taylor has played 11 NFL seasons, all with Miami, and he has started every game each of the past eight years.
"I love Miami [and] will always cherish my 11 years with the Dolphins," Taylor said in a statement. "Having said that, I'm looking forward to meeting with Mr. Snyder and getting to know my new coaches and teammates. I'm just proud to be representing our nation's capital as a Redskin."
He had 11 sacks during the 2007 season, giving him 117 in his career.
"His play speaks for itself," Cerrato said. "I think it's easy to talk about Jason Taylor. He's got statistics and everything else to back up everything that he's done."
Taylor has said he planned to play only one more season.
But Cerrato said: "I'm 100 percent positive he'll play longer than one year."
Taylor's agent, Gary Wichard, said it's possible Taylor will play beyond the coming season.
"The Dolphins got real good value for Jason," Wichard said. "And he's excited about going to Washington -- he wanted an opportunity to compete in the playoffs in 2008. At the same time, this is the end of his years with the Dolphins, so it's kind of bittersweet."
The Dolphins released statements from new general manager Jeff Ireland and owner Wayne Huizenga thanking Taylor for his contributions. There was no comment from Parcells.
"Ever since he joined the team as a rookie, he has been outstanding on the field and a leader in our community," Huizenga said. "Whether it was his intensity between the lines or his commitment to his charitable works, he made a lasting impact here."
Last season, Taylor was chosen NFL Man of the Year and was the lone Pro Bowl player for a Dolphins team that went 1-15. His departure is the latest move in a major roster shakeup.
In Miami, Taylor played primarily at right end, but Cerrato said Washington will move him to the left side, where Daniels was the starter. Andre Carter plays right defensive end for the Redskins.
Wichard said he first became aware the deal might happen Sunday morning.
"When we heard Daniels went down, that started it on a fast track," Wichard said.
Daniels, a starter, was hurt on the initial play of 7-on-7 offense versus defense drills on Sunday. He stayed down on the turf for several minutes before being taken away on a cart, a towel draped over his head. He's expected to have surgery Friday.
"Not a good way to start, at all," middle linebacker London Fletcher said. "It's a big blow to our defense. Phil was a tremendous leader, excellent at playing the run, and was going to be our third-down attack guy. With him going down, it's like we're replacing two guys."
ESPN.com's John Clayton first reported Daniels' season-ending injury and the fact that the Redskins were pursuing Taylor.
Cerrato said Taylor is expected to report to Redskins training camp on Monday -- something the player's agent confirmed.
The Redskins also lost another defensive end, reserve Alex Buzbee, to a season-ending injury during their afternoon practice. Buzbee ruptured his Achilles tendon.
"With Phillip gone, and now Buzbee gone, there's a hole there," coach Jim Zorn said. "And Phillip has created a big hole."
Day 1 of Zorn's training camp debut as an NFL head coach also included this sight: Cornerback Fred Smoot threw off his left shoe and clearly was in pain after wideout Santana Moss landed on him during the afternoon practice. It turned out Smoot sprained his ankle and is expected to miss only a week or less.
"I love sprained ankles now, because we know that's just a few days' deal," Zorn said, cracking a smile.
He was more serious while speaking about the loss of Daniels, who has played 12 seasons in the NFL with Washington, Chicago and Seattle. His 59 career sacks rank 17th among active players.
"The hard part is he was so ready, and he did everything that he could possibly do to not just have a great training camp but an excellent football season," Zorn said. "And now he's got a new challenge before him, and of course we have a new challenge before us."
The Redskins began training camp with Erasmus James sidelined. He's a former first-round pick who has had serious knee injuries, and Zorn said he doesn't expect James to be able to begin practicing until next month.
Information from ESPN.com senior NFL writer John Clayton and The Associated Press was used in this report.