The Blackhawks dealt Bolland -- who notched three goals and three assists in 18 post-season appearances in Chicago's march to the NHL championship -- to the Maple Leafs for two picks in the ongoing 2013 draft and a 2014 fourth-round draft choice.
Bolland endeared himself to Blackhawks fans by netting the winning goal late in regulation during the decisive Game 6 of the Stanley Cup Finals in Boston.
Meanwhile, the team signed Bickell, another playoff hero, to a four-year contract.
The 27-year-old pending free agent, who amassed nine goals and 17 points over 23 post-season games for Chicago, inked a deal worth a reported $16 million.
The second-round 2004 Blackhawks pick has compiled 40 goals and 50 assists over 220 career regular-season games with the squad.