The team announced the moves Friday.
The 37-year-old Brunette has 256 goals, 450 assists and 706 points in his career and was third on the Minnesota Wild with 46 points (18 goals, 28 assists) while appearing in all 82 games last season. A 15-year veteran, he has played in more games (970) than any other NHL player since the start of the 1998-99 season and has missed just two over the last eight regular seasons.
Mayers, who is 36, had three goals and 11 assists in 78 regular-season games with the San Jose Sharks last season. He also appeared in 12 playoff games.
The 32-year-old McLean had 27 points (10 goals, 17 assists) last season in 50 games with Bern of the Swiss League, where he spent the past two years. The 39-year-old O'Donnell had 17 assists and 18 points for the Philadelphia Flyers last season, his 16th.
Earlier this week, the Blackhawks agreed to a four-year contract with defenseman Steve Montador.