The 26-year-old Edmondson, who will join up with the Reds in November, left Saints last year to play in Australia.
But Edmondson was recently told he would be released halfway through his two-year contract.
"Mark's a quality player. He was one of the best front rowers in the league and I believe he's better now," said Reds football director Steve Simms.
"He will give us a new dimension as he is determined, strong and powerful. We're pretty excited to have landed him."
St Helens were reported to have been interested in re-signing Edmondson.