Campbell, who was a member of the Chicago's 2010 Stanley Cup championship team, scored 27 points in 65 games last season and had a plus-28 rating. Olesz scored 17 points in 44 games for Florida.
"Brian is a top-four, mobile, puck-moving defenseman who we are very pleased to have acquired, Florida General Manager Dale Tallon said on the team's website (panthers.nhl.com).
"He is a hard working and responsible player, who will be counted on to play an important role on our power play. We look forward to his immediate contribution to our club."
Local media reported that Florida needed to add salary to raise its payroll above the League mandated minimum of $48.3 million.
Campbell has five years remaining on his contract at $7.1-million per season while Olesz has three years left on his contact for $3.125-million per season.
(Reporting by Mike Mouat in Windsor, Ontario. Editing by Patrick Johnston)