The Rangers will receive forwards Ryan Spooner and Matt Beleskey, prospect defenseman Ryan Lindgren, the Bruins' 2018 first-round draft pick and a 2019 seventh-round pick.
New York will retain 50 percent of Nash's remaining salary for this season, according to TSN.
In early February, the Rangers asked Nash for a list of 12 teams he would allow to be traded to as part of his modified no-trade clause. The team later submitted an open letter that hinted New York would be moving some of its "familiar faces."
Nash, 33, will rejoin Nick Holden in Boston, as the Bruins acquired him in a trade last week. The Rangers also traded Michael Grabner ahead of Monday's trade deadline. Nash carries an annual cap hit of $7.8 million.
This is the second time Nash has been traded in his career. He was part of a 2012 offseason trade that landed him with the Rangers after nine seasons with the Columbus Blue Jackets.
Information from ESPN's Emily Kaplan was used in this report.