The Bolts acquired the 29-year-old with J.T. Miller for Vladislav Namestnikov, Brett Howden, Libor Hajek, Tampa Bay's first-round pick in the 2018 draft and a conditional second-round pick next year. Tampa gave up the haul while battling for the best record in the league.
The Lightning ended up losing in the conference finals to the eventual champion Capitals.
McDonagh, a two-time All-Star, had two goals and 24 assists in 49 games for the Rangers last season and two goals and an assist in 14 regular-season games in Tampa. He added five assists in the playoffs.