Galloway agreed to a one-year contract that will give the 38-year-old wide receiver a chance to play his 16th NFL season, sources said.
Galloway will try to win a spot on the Redskins' roster when Washington gathers for its next minicamp in two weekends. The Redskins have been looking for another veteran wide receiver, and they believe Galloway has the chance to provide them with some long plays.
The former Ohio State receiver has 689 catches for a 15.6 yards per catch average during an NFL career that began in 1995, but he hasn't had a TD catch since making six for the Tampa Bay Buccaneers in 2007. He has only 20 catches over the last two seasons combined.
From 2004 to 2008, Galloway and Redskins general manager Bruce Allen worked together for the Buccaneers.
While together in Tampa, Galloway caught at least five touchdown passes in each of the first four seasons they spent together.
Wade, a seven-year veteran, has played in 102 career games with 50 starts for the Bears, Titans, Vikings and Chiefs. He has 244 career receptions for 2,858 yards and nine touchdowns, as well as 1,194 yards on 50 career kickoff returns.
Adam Schefter is ESPN's NFL Insider. Information from The Associated Press was used in this report.