Withey has a strong chance to make the Jazz's opening-night roster, which currently includes 13 guaranteed contracts.
Withey's deal includes a team option in the second year, a league source told Yahoo.
Withey, 25, played his first two NBA seasons with the New Orleans Pelicans, where he averaged three points and 2.3 rebounds.
After leaving Kansas, Withey was the 39th overall pick to the Portland Trail Blazers in the 2013 NBA draft. He was moved to New Orleans in a three-way deal that helped bring Robin Lopez to the Blazers.