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.
Zibanejad was the No. 6 overall pick in the 2011 NHL draft by the Ottawa Senators, but the Sens dealt him to New York last year for forward Derick Brassard.
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.