Dundon, 46, is chairman and managing partner of Dundon Capital Partners, a Dallas-based private investment firm.
Commissioner Bettman said he is confident that the NHL has the right man for the job.
"You could see it today," Commissioner Bettman said. "He's the real deal. He's down-to-earth, he's really smart, he's really passionate and emotional. He's going to create an organizational culture in his image. I think that's going to be exciting for the franchise."
Karmanos had owned the team since 1994, when he purchased the Hartford Whalers. He moved them to North Carolina in 1997, when they were renamed. They played in Greensboro for two seasons before moving to Raleigh.
Karmanos was inducted into the Hockey Hall of Fame in the category of builder in 2015.
As for Dundon, Karmanos said, "I knew from the first time I first talked to Tom that he was the real deal and would be a good owner."
NHL.com correspondent Kurt Dusterberg contributed to this report.