The 30-year-old forward is in the final season of a two-year contract and can become an unrestricted free agent July 1.
New York will receive defenseman prospect Yegor Rykov and a second-round pick in the 2018 NHL Draft.
Grabner has 31 points (25 goals, six assists) in 59 games this season. He was scratched from a 3-1 loss at the Montreal Canadiens on Thursday.
He has 244 points (156 goals, 88 assists) in 532 games during nine NHL seasons with the Rangers, Toronto Maple Leafs, New York Islanders and Vancouver Canucks. He has scored at least 20 goals four times.
Selected by Vancouver in the first round (No. 14) in the 2006 NHL Draft, Grabner has 12 points (six goals, six assists) in 29 Stanley Cup Playoff games.
Rykov, 20, was a fifth-round pick (No. 132) in the 2016 NHL Draft. He is playing in the Kontinental Hockey League this season.
New Jersey, which lost to the Minnesota Wild 4-2 on Thursday, leads the Columbus Blue Jackets by five points for the first wild card into the Stanley Cup Playoffs from the Eastern Conference.