New Jersey shipped defenseman prospect Yegor Rykov and a second-round pick in this year's draft to New York.
Grabner was scratched from the Rangers' 3-1 loss to the Montreal Canadiens on Thursday.
The veteran forward leads New York with 25 goals and six assists. There have been only three players in the last 40 years to have a season with 25-plus goals and single-digit assists, according to ESPN Stats & Information.
Grabner, set to be an unrestricted free agent after the season, leaves a Rangers team that is 27-29-5 and has made no secret that it planned to unload talent ahead of Monday's trade deadline.
Earlier this month, the Rangers hinted in an open letter that major changes could be coming as the franchise sought "young, competitive players that combine speed, skill and character" while admitting that the team could lose some "familiar faces."
The Rangers, who have made the playoffs in 11 of the past 12 seasons, began reshaping their roster over the summer by trading veteran center Derek Stepan and top backup goalie Antti Raanta to the Arizona Coyotes to relieve cap space and buying out the final three seasons of defenseman and alternate captain Dan Girardi's contract.
The 20-year-old Rykov has 2 goals, 12 assists and a plus-13 rating in 51 games for SKA Saint Petersburg of the KHL this season.
Information from ESPN's Emily Kaplan and Greg Wyshynski was used in this report.