Hornqvist, 33, has three years remaining on his current deal, which carries an annual cap hit of $5.3 million.
The gritty Swede was on pace to eclipse the 20-goal mark over 82 games for the eighth time of his career this season after recording 17 goals and 32 points through 52 contests. Hornqvist captured back-to-back Stanley Cups with the Penguins in 2016 and 2017, scoring the championship-clinching goal in the latter year.
Matheson, 26, is under contract through the 2025-26 campaign and carries an annual cap hit of $4.88 million. The 6-foot-2 rearguard recorded eight goals and 12 assists through 59 games this season.
The Penguins' acquisition of Matheson comes just weeks after general manager Jim Rutherford said the club would be moving on from defenseman Justin Schultz. The pending unrestricted free agent's latest deal was worth $5.5 million annually.
Sceviour, 31, contributed six goals and 16 points while ranking third on the Panthers with 91 hits in 69 games this season. He has one year remaining at $1.2 million on his current deal.
The trade marks Bill Zito's first splash as the Panthers' GM. Florida hired the 56-year-old on Sept. 2 after mutually parting ways with Dale Tallon in August.