The Rangers traded the former US Olympic national team member and forward J. T. Miller to the Lightning in exchange for Czech defenseman Libor Hájek, Canadian centre Brett Howden, Russian forward Vladislav Namestnikov, a 2018 first-round draft pick, and a second-round draft pick.
The Lightning announced the deal on their website Monday.
One of the older players available at the deadline, the 28-year-old McDonagh has one year remaining on a six-year contract he signed with club.
In 49 games this season, McDonagh has two goals and 26 points.
The 24-year-old Miller has 13 goals and 40 points in 63 games with the Rangers this season.
The Lightning hope the move bolsters their playoff run as they lead the Eastern Conference standings with 87 points through 62 games this season.
Two-time all-star McDonagh had spent all seven of his previous NHL seasons with Tampa Bay.
Both McDonagh and Miller are former first-round draft picks. McDonagh was taken 12th overall by the Montreal Canadiens while Miller was selected 15th overall by the Rangers.
Elsewhere, the Winnipeg Jets made two moves prior to the NHL trade deadline.
Winnipeg acquired forward Paul Stastny from the St. Louis Blues for forward Erik Foley and two draft picks. The Jets then traded for defenceman Joe Morrow from the Montreal Canadiens for a 2018 fourth-round draft pick.
Winnipeg sent a 2018 first-round pick and a fourth-round 2020 selection to the Blues.
Stastny, 32, had 12 goals and 28 assists in 63 games this season with St. Louis. He is the son of Hockey Hall of Famer Peter Šťastný.
Also, the San Jose Sharks acquired Evander Kane of the Buffalo Sabres in exchange for a conditional first-round pick in 2019, a fourth-round pick in 2020, and forward Dan O’Regan to the Sabres in the deal.
The 26-year-old has 20 goals and 20 assists in 61 games with the Sabres this season.
Kane is in the final season of a six-year, $31.5 million (RM123.1 million) contract and will become an unrestricted free agent during the offseason.
The one player that didn’t get moved but many thought might was Swedish star Erik Karlsson. The Ottawa Senators decided to keep the All-Star defenseman after listening to several offers.