The six-time Pro Bowl defensive end - who was the 2006 NFL Defensive Player of the Year - fell out of favor in Miami after spending his offseason on the TV show "Dancing With the Stars" rather than working out with teammates.
The deal came about nine hours after starting defensive end Phillip Daniels was carted away from the practice field at Redskins Park with a season-ending left knee injury on Day 1 of training camp.
It also came only about 1 1/2 hours after Washington executive vice president Vinny Cerrato told reporters: "We haven't talked to anybody about anything."
Cerrato said Taylor is expected to report to training camp on Monday.
"We're fortunate there was a guy that caliber on the market when somebody got hurt," 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 and he's started every game each of the past eight years.
He had 11 sacks during the 2007 season, giving him 117 over his career.
"His play speaks for itself. 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," Cerrato said.
Taylor has said he planned to play only one more season.
But Cerrato said Taylor has two years left on his contract and added: "I'm 100 percent positive he'll play longer than one year."