O'Byrne, 26, had appeared in only three games for the Canadiens this season. The 6-foot-5, 234-pound defenseman was Montreal's third-round pick (79th overall) in the 2003 entry draft.
He played in in a career-high 55 games last season (four points) and 13 of Montreal's 19 games during its surprising playoff run.
O'Byrne becomes a restricted free agent this summer, and the deal trims $1.4 million from Montreal's payroll.
"Ryan is another young defenseman who will add size and depth to our team," Avalanche general manager Greg Sherman said in a team statement.
The Avalanche have 10 injured players overall, including star goalie Craig Anderson.
Bournival, 18, has a team-leading 24 points (10-13) in 17 games with the Quebec Major Junior Hockey League's Shawinigan Cataractes. He was drafted 71st overall by the Avalanche in June's NHL entry draft.
He also played for Canada in the world under-18 championship in 2009, scoring two goals and an assist in six games.
Information from The Associated Press was used in this report.