The announcement was made in Helsinki, where the Panthers faced the Chicago Blackhawks in their season opener. Terms of the deal were not disclosed.
The 50-year-old Sexton joined the organization in January 2007 and previously served as Florida's assistant GM. He oversaw the team's contract negotiations, scouting, administration and player development after Jacques Martin left to coach the Montreal Canadiens in June.
During his tenure with the Panthers, Sexton has helped the club re-sign restricted free agents like center Stephen Weiss and left wing David Booth, who agreed to a six-year contract extension this summer.
Sexton also helped Florida ink deals with goalie Scott Clemmensen, veteran center Steve Reinprecht and defenseman Jordan Leopold this offseason.
"Over the past two seasons, our club has been successful in re-signing several of our core players to multiyear contracts, while also acquiring numerous high character, hardworking free agents who have helped to create our team identity and the framework for success," Sexton said in a statement. "We have made significant strides over the last two seasons and our fans should be excited about our team."
After Martin left for Montreal, Sexton worked with Florida's first team president, Bill Torrey, who also led the Panthers' general manager search. Martin was the Panthers' general manager the past three seasons and coached the team from 2004-08.
Sexton also spent eight years with the Ottawa Senators, where he served as president, CEO and general manager while laying the foundation for the team's future success.
Panthers president Michael Yormark said in a statement that Sexton is "ideal individual" to take over as general manager.
"Randy possesses all the necessary qualities to be a successful general manager in the National Hockey League and he has done a tremendous job over the past two seasons in shaping our team through the draft, free agency and trades," Yormark said. "He has a vast knowledge of our entire organization and we are confident that, along with head coach Pete DeBoer, our club is positioned for success."
Associated Press Writer Sarah Larimer in Miami contributed to this report.