The forward gets a four-year deal, with an annual salary cap hit of $4.2 million, a source told ESPN.com's Scott Burnside.
"It's always positive to be able to resolve a contract," said Dubinsky's agent, Kurt Overhardt. "It's a four-year term and it's something my client wanted to do which is stay in New York and keep playing his role as a member of the team and we're very proud. I felt that the team felt the same way. We worked hard and we got positive results."
Dubinsky would have been the first player to have an arbitration hearing this offseason. Hearings were scheduled to begin Wednesday, but the other players already had agreed to terms with their teams. Overhardt said he and Dubinsky weren't afraid of heading to arbitration, but the goal is to try to resolve the contract dispute and work with the organization to please both parties.
Dubinsky led the Rangers last season in goals (24), assists (30) and points (54), all of them also career highs. He is expected to be one of the team's top offensive threats next year and assume a greater leadership role this after the buyout of former captain Chris Drury. Dubinsky will also be one of the longest-tenured current Rangers on what is primarily a young team.
The Rangers and Dubinsky previously have had extended contract negotiations. In 2009, Dubinsky staged an eight-day holdout that carried over into training camp before signing a two-year deal worth $3.7 million that ended at the end of this past season. When Dubinsky's new deal ends, he will be just 29, which would allow for him to possibly sign another large contract with a team.
"The term was important for both parties," Overhardt said. "He's a young guy. He's going to be a young guy at the end of the deal and it's a good and positive thing."
The 25-year-old forward was one of four Rangers restricted free agents to file for salary arbitration and the third to come to terms with the team before arbitration.
Forward Brian Boyle and defenseman Michael Sauer both have re-signed. Forward Ryan Callahan, who is another long-tenured Ranger expected to step into a greater leadership role this upcoming season after serving as an alternate captain last year, is scheduled to have an arbitration hearing July 28.
The Rangers also agreed to terms with restricted free-agent forward Artem Anisimov, who was not eligible to file for arbitration because he did not meet the playing time requirements.
The Rangers selected Dubinsky in the second round of the 2004 draft with the 60th pick. In five seasons, Dubinsky has scored 71 goals and has 108 assists in 316 career games.
"Brandon is incredibly excited," Overhardt said. "It's an exciting time in his career and his life and he deserves it."
Matt Ehalt is a regular contributor to ESPNNewYork.com. ESPN.com's Scott Burnside contributed to this report.