Pouncey and Stephens-Howling suffered ACL tears on Sunday while Foote sustained a torn bicep.
The Steelers opted to sign a kicker instead of another linebacker because Shaun Suisham is dealing with a hamstring injury, though he was able to play through it on Sunday.
Dwyer led the Steelers in rushing last season (623 yards) but he was the odd man out when the team trimmed its roster to 53 players on Aug. 31. The fourth-year veteran rejoins a running back group that is without Le'Veon Bell as the rookie recovers from a mid-foot sprain and struggled against the Titans. The Steelers averaged just 2.1 yards on 15 carries in the 16-9 loss to the Titans.
Bell has said he hopes to play in Week 2, but the former Michigan State star also acknowledged that's a best-case scenario and said he won't return until fully healthy.
Velasco started every game last season for Tennessee -- three of those came at left guard -- but he became expendable after the Titans signed a free-agent center and drafted one in the offseason.
The well-traveled Graham will kick for his ninth NFL team. His field goal percentage (85.4) is seventh-best in league history.
The Steelers play at Cincinnati next Monday night.