Stephens, 24, struggled to find a role on a deep Lightning squad. He has appeared in just 45 NHL games over the past two seasons, including seven last year. He is signed for one more season at an AAV of $737,500.
On the rebuilding Red Wings, Stephens will slot into a hole created by the departure of depth centre Luke Glendening, who signed with the Dallas Stars in free agency.
Red Wings general manager Steve Yzerman drafted Stephens with a second-round pick in the 2015 NHL Draft.