Bowness, 58, spent the last seven seasons on Alain Vigneault's staff with the Vancouver Canucks, most recently as associate coach. Vigneault and Bowness were relieved of their duties on May 23.
"With 24 years of NHL coaching experience as both a head coach and an assistant, we are confident Rick will be a valuable addition," Lightning general manager Steve Yzerman said in a statement.
Bowness has served as a hired head coach for Boston, Ottawa and the New York Islanders, and coached on an interim basis for Winnipeg and Phoenix.
Prior to his coaching career, the Moncton native played 173 games in the NHL as a forward with the Atlanta Flames, St. Louis, Detroit and Winnipeg.
Bowness will serve as assistant to Jon Cooper, who succeeded Guy Boucher in March as Tampa Bay coach.