Lightning general manager Julien BriseBois announced the move Tuesday, selecting Blashill to replace Derek Lalonde on coach Jon Cooper's staff. Lalonde was hired to replace Blashill in Detroit.
Blashill, 48, coached the Red Wings the past seven seasons, compiling a 204-261-72 record. Detroit missed the playoffs in six of the seven seasons.
With the Lightning, Blashill joins a staff that includes assistant coaches Jeff Halpern and Rob Zettler, goaltender coach Frantz Jean and video coaches Nigel Kirwan and Brian Garlock.
The two-time defending champion Lightning were dethroned last month by the Colorado Avalanche in the Stanley Cup Final.