Sweed was placed on injured reserve Monday with a non-football-related illness. Coach Mike Tomlin would not reveal any details of Sweed's condition Tuesday.
"I think it's appropriate right now that we say very little in regard to his personal issues," Tomlin said. "He has our full support. Anything else I say will be in regards to protecting his privacy."
Galloway was cut by the New England Patriots earlier this season after catching seven passes for 67 yards. The former Ohio State receiver has 689 catches for a 15.6 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.
Pittsburgh was interested in signing Galloway during the offseason, but he chose New England instead. Galloway, 38, grew up in Bellaire, Ohio, which is 60 miles from Pittsburgh.
The Steelers also signed long snapper Jared Retkofsky to replace Greg Warren, who injured a right knee ligament on the final play of Pittsburgh's win over the Green Bay Packers. Retkofsky was the Steelers' long snapper for the final two months and the playoffs last season after Warren tore a knee ligament.
Retkofsky had been playing for the New York Sentinels of the United Football League.