A source told ESPN.com that Stepan signed a six-year deal that will have an average annual value of $6.5 million.
The two sides had been set for an arbitration hearing Monday morning in Toronto.
"For the most part, both sides were pretty close to begin with. These things just do take time, setting up everything," Stepan said on a conference call Monday. "Both sides are very happy and comfortable where the deal was at."
"There wasn't any bad blood through the whole thing," he added. "... It went the way I expected it to, and it went the way I wanted it to."
Stepan, 25, finished the 2014-15 season with 16 goals and 55 points. He is the first Rangers center to score 50 points or more in three consecutive 82-game seasons since Wayne Gretzky.
On being a core member of the team for years to come, Stepan said, "We have a great group of guys. That's where it really starts. How close our teams have been the last four or five years has a lot to do with the group of guys we have in the [locker] room. We've got a competitive group, and there's nothing but exciting things to come for us moving forward."