"Tomas Plekanec proved to be one of our most consistent players last season," Habs GM Bob Gainey said in a statement. "He established career highs in all categories and his defensive play was extremely efficient. He is young, dynamic and we strongly believe he is ready to take on more responsibilities with our club."
Plekanec, 24, ranked fourth on the team with 47 points (20-27) in 81 games in his second NHL season. He also led the team with a plus-10 rating.
Biron, 27, was acquired from the San Jose Sharks in return for defenceman Patrick Traverse last December. He led the AHL's Hamilton Bulldogs in scoring last season with 39 points (10-29) in 77 games between Worcester and Hamilton and posted a plus-16.
Rivers, 32, split last season between the St. Louis Blues, recording a goal and three assists, and the Peoria Rivermen, the team's AHL affiliate, where he had 23 points (4-19).
The Canadiens also signed forward Cory Urquhart, 22, and defenceman Marvin Degon, 24, to one-year contracts.