Long-term target Flo, 29, moves to the Stadium of Light on a three year deal while Stewart has also signed a three year deal but with the option of an extra year.
Both Flo and Stewart signed in time to be available for selection for tomorrow's Premiership match against Manchester United and Reid has confirmed that both players will be in his squad to face United. He said: "I've had a chat to both players and it's not a problem.
"Mind Marcus trained with us today and finished last. Jason McAteer asked me if I'd signed Rod Stewart!"
Flo has won 63 caps for Norway, scoring 21 goals, and joined Rangers from Chelsea two years ago for £12million.
Reid said: "There's now good competition in all areas of the squad and I'm glad we've got Tore and Marcus. I've been working like a mad man to try to get them in.
"When you look at Flo, Stewart, Phillips, Quinn, Kyle, Piper and Bellion, we're now strong in that department.
"Marcus is a player I've had my eye on for a long time and when I found out of his availability I wasted no time trying to sign him.
"He's got great ability in and around the box and is a clever and ambitious player. He's scored goals at every level."
Todays signings brings the Sunderland manager's close-season spending to close on £16million.