Cooper had been coaching Syracuse of the AHL, Tampa Bay's top minor league affiliate. He is replacing Guy Boucher, who was fired Sunday after 2 1/2 years with the team.
"He has had success at every level he has coached and is extremely familiar with our organization, as well as our players," Tampa Bay general manager Steve Yzerman said in a statement. "He has a tremendous record at all levels and we feel he is ready to make the move to the NHL."
The Lightning, at 13-18-1, are in next to last place in the Eastern Conference and appear headed to missing the playoffs for the second consecutive season.
Cooper will coach his first game for the Lightning on Friday night against the New Jersey Devils.
"There is no other team in hockey that I would rather be coaching than the Tampa Bay Lightning," Cooper said in a statement.
"It's quite a tribute to Steve Yzerman, (owner) 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."
The 45-year old Copper also coached at Norfolk of the AHL when it was a Lightning minor league team from 2010-12. His AHL record is 133-62-26.
Ten players on Tampa Bay's roster, including rookie centre Cory Conacher, who has nine goals and 23 points, played for Syracuse this season.
Dan Lacroix and Steve Thomas will handle coaching duties when the Lightning host the Buffalo Sabres on Tuesday night. The pair will then remain as assistant coaches for Cooper.
Syracuse assistant Rob Zettler will take over for Cooper in the minors. Lightning assistant coach Martin Raymond will join Zettler's staff.
Raymond and Lacroix coached Tampa Bay on Sunday in Winnipeg when the Lightning lost 3-2 to the Jets.
Tampa Bay entered this season with playoff aspirations after adding goalie Anders Lindback and defencemen Sami Salo and Matt Carle. Lindback and captain Vincent Lecavalier have been among the players sidelined by injuries.Suggest a correction