The financial terms were not disclosed by the club, although Frank Seravalli of Daily Faceoff reported it's a $22.666-million deal ($5.65-million average annual value).
Shesterkin, whose cap hit in 2020-21 was $925,000, was a restricted free agent, but did not file for arbitration.
The 25-year-old from Moscow emerged as the starter this past season after the Rangers parted ways with Henrik Lundqvist. Shesterkin posted a 16-14-3 record, including two shutouts, and registered a 2.62 goals-against average and .916 save percentage.
Overall, Shesterkin holds a 23-12-3 record, 2.59 GAA and .921 save percentage over the past two seasons. He was a fourth-round pick, 118th overall, in 2014.