The deal announced Wednesday would keep Kuemper in the desert through the 2021-22 season.
The 29-year-old Kuemper had been a career backup until Arizona's No. 1 goalie Antti Raanta suffered a season-ending injury last year.
Kuemper was 27-20-8 with a 2.33 goals-against average and .925 save percentage.
He went 22-9-6 with a 2.05 goals-against average after January as the Coyotes made a playoff push. Arizona fell four points short of the final Western Conference playoff spot.
Kuemper is expected to share time with Raanta this season.