A league source told ESPN NFL Insider Adam Schefter that Davis signed a one-year deal.
On Thursday night, media reports said Davis did not make a trip to meet with the New York Jets, one of the teams reported to be courting him.
Davis has played for the Redskins since being drafted by the team in 2008, and he had met earlier in the week with the Buffalo Bills.
He was the Redskins' leading receiver with 24 catches for 325 yards before tearing his Achilles' tendon against the Giants this past October.
He recently told the NFL Network that he is recovering well from the injury and that he is even "a little bit ahead of schedule."
In 2011, he was having a career year with 59 catches for 796 yards before being suspended for the final four games after failing multiple drug tests.
The 27-year-old tight end has 155 catches, 1,973 yards and 12 touchdowns in 62 career games.