Hoak, a 2016 three-star prospect at Dublin Coffman in the Columbus suburbs, played in five games last season for the Wildcats.
He completed 13 of 26 passes for 167 yards and two touchdowns for the Blue and White and will bring two seasons of eligibility with him to Columbus.
On Friday night, California high school quarterback J.P. Andrade announced he will attend Ohio State as a preferred walk-on next season.
They will join a position group that already consisted of sophomore-to-be Justin Fields, senior Chris Chugunov and redshirt freshman Danny Vanatsky, a walk-on from Cincinnati Hills Christian Academy.
Fields and Baldwin competed for the starting job in spring.
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Although Day declined to name a starter after the spring game, Fields appeared to get the majority of No. 1 reps and was widely expected to win the job after transferring from Georgia in January.
Chugunov arrived last summer as a graduate transfer from West Virginia.