Cooper, 45, was coaching Tampa Bay's affiliate in the American Hockey League, the Syracuse Crunch. Syracuse currently has the best record in the AHL at 39-18-3-5.
"We are very pleased to introduce Jon as our head coach today," Lightning general manager Steve Yzerman said. "He has had success at every level he has coached and is extremely familiar with our organization, as well as our players. He has a tremendous record at all levels and we feel he is ready to make the move to the NHL."
For the two seasons prior to 2012-13, Cooper was coach of the Norfolk Admirals, which was Tampa Bay's AHL affiliate at the time. In 2011-12, Cooper led Norfolk to a franchise-record 55 wins and the Calder Cup. Norfolk finished the season on a 28-game winning streak. After the season, Cooper was given the Louis A.R. Pieri Memorial Award as the most-outstanding coach in the AHL.
Tampa Bay relieved Guy Boucher of the coaching duties early Sunday morning after he had led the Lightning to a 13-17-1 mark through 31 games. In 2011, Boucher led the Lightning to within one game of the Stanley Cup Final in his first season with the club. The Lightning are currently 14th in the Eastern Conference following a 3-2 loss to the Winnipeg Jets on Sunday night.
Cooper will reportedly be introduced at a press conference Wednesday.
"There is no other team in hockey that I would rather be coaching than the Tampa Bay Lightning," he said in a statement released Monday night. "It's quite a tribute to Steve Yzerman, Jeff Vinik and the organization they are building that they are proud to promote from within. I look forward to getting to know the players and getting to work right away."