Ducey, a former Cold Stone Creamery chief executive, was backed by numerous national tea party leaders including Sarah Palin and Sens. Ted Cruz (R-Tex.) and Mike Lee (R-Utah).
The Associated Press has called the race for Ducey. He will be favored to defeat Democrat Fred DuVal, who was unopposed in the primary.
Smith, a more moderate Republican, had Brewer’s backing. The governor campaigned hard for him in the closing stage of this race.