Wennberg, 26, was recently bought out of the final three seasons of a six-year, $29.4-million extension he signed with the Columbus Blue Jackets after the 2016-17 campaign.
"Alexander is a talented forward who plays the game with great pace and skill," Panthers general manager Bill Zito said in a team statement. "His speed and offensive capability will be an excellent addition to the strength of our forward group."
The 2013 14th-overall pick is coming off a five-goal, 22-point campaign in Columbus last season – his lowest point total since his rookie campaign in 2014-15.
The Stockholm native's best season came in 2016-17, during which he scored 13 and racked up 46 assists in 80 games, earning his contract extension.