The 48-year-old joins coach Jon Cooper's staff with assistants Jeff Halpern and Rob Zettler after he coached the Detroit Red Wings for seven seasons.
Blashill replaces Derek Lalonde, who was hired as Red Wings coach June 30.
The Lightning advanced the Stanley Cup Final this season but lost the best-of-7 series to the Colorado Avalanche in six games after winning the Stanley Cup each of the previous two seasons.
Detroit failed to make the Stanley Cup Playoffs in six seasons of Blashill's tenure. He was the second longest-tenured coach in the NHL behind Cooper (10 seasons).
"Jeff did an outstanding job of leading this organization in very, very difficult circumstances," Red Wings general manager Steve Yzerman said June 30. "I've said this before, but you can't judge Jeff Blashill on his Detroit Red Wings record. You have to judge him on how he ran this program and conducted himself in an extremely professional way. It is really unfair to put all of this on him."
Blashill was 204-261-72, ranking sixth in Red Wings history in wins and fifth in games coached (537). He was hired June 9, 2015 to replace Mike Babcock, who left for the same position with the Toronto Maple Leafs on May 20, 2015.
In Blashill's first season, Detroit made the playoffs, a five-game loss to Tampa Bay in the Eastern Conference First Round. The Red Wings have not qualified or finished higher than fifth in their division since. They were 32-40-10 this season and finished sixth in the Atlantic Division, 26 points out of a playoff spot.
