The deal was finalized late Friday, after the first round of the NHL draft.
The 32-year-old Campbell had 19 goals and 38 assists over three seasons with the Blackhawks.
He was the third-highest paid player on the team last season at $7.142 million behind Duncan Keith and Marian Hossa. Campbell just completing the third year of an eight-year contract that will pay him more than $56 million. He had five goals and 22 assists in 65 games last season, averaging nearly 23 minutes per game.
The 25-year-old Olesz was the seventh overall pick by the Panthers in the 2004 draft. The native of the Czech Republic had six goals and 11 assists in 44 games last season, completing the third of a six-year contract that pays him $18.75 million.
"We're fortunate in our organization that we've got a lot of young players who we need to find spots for," general manager Stan Bowman said, adding: "We're excited that we added a first-round pick. It's not easy to do that these days the way those are valued around the league."