Zibanejad—who was a restricted free agent prior to signing the deal—will earn an average annual salary of $5.35 million.
Coming to terms also allowed the Rangers and Zibanejad to avoid arbitration ahead of Tuesday's deadline.
The 24-year-old forward is coming off his first season as a member of the Rangers, and it was a productive one.
Although he missed 26 games due to injury, Zibanejad still finished with 14 goals and 23 assists for 37 points to go along with a plus-nine rating. He also added nine points in 12 playoff contests.
The Sweden native's best season came in 2015-16, when he set career highs with 21 goals and 30 assists for 51 points in Ottawa.
Had Zibanejad played a full season in 2016-17, projections would have put him at a new career high of 54 points.
Zibanejad represents the final significant internal chip to fall for New York this offseason, as it agreed to a deal with forward Jesper Fast earlier this month.