Zednik, a left wing, agreed to a two-year contract and McLean, a centre, gets a three-year deal.
The 31-year-old Zednik has played in 621 career games for Washington, Montreal, and the New York Islanders, recording 320 points. Last season, while playing for both Washington and the New York Islanders, he scored 21 points in 42 games.
The Slovakia native has represented his country in seven international competitions, including the Olympics and three world championships.
McLean posted career-high marks last season with 15 goals and 20 assists in 78 games for the Colorado Avalanche. He has 106 points in 238 NHL games during his four year career with Colorado and Chicago.