The schools announced the contract Friday.
The Utes will make the trip to Gainesville to start the series, and Florida will travel to Utah the following year.
It's the latest step in Florida's quest to improve its nonconference schedules. The Gators are playing two teams from the Football Championship Subdivision this fall, and their 2020 schedule includes visits from Eastern Washington, South Alabama and New Mexico State.
But athletic director Scott Stricklin has taken a more aggressive approach to future schedules, signing contracts in the past 15 months to face South Florida (2022, '23, '25), Miami (2024-25), Colorado (2028-29) and Texas (2030-31).
Florida and Utah played once previously: the Gators won 38-29 in Gainesville in 1977.