That announcement is expected Thursday or possibly Friday, with Wieland possibly meeting the team in Los Angeles for the start of a three-game series on Friday afternoon.
"It's not out of reason to think Joe will make that start," manager Bud Black said, smiling.
Wieland, considered one of the Padres top prospects, was pulled from his start Tuesday while pitching for Tucson and was told by manager Terry Kennedy that he was heading to the big leagues.
Wieland's start comes on the day the Padres will need their fifth starter for the first time this season.
In two starts with Tucson, the 22-year-old was 0-1 with a 3.52 ERA in 7 2/3 innings. He had two walks and 11 strikeouts in that stretch.
"You like the arm and like the delivery," Black said of Wieland. "In the spring, we saw a guy who has four pitches. I liked his composure and he looked like a well-rounded player. He showed poise on the mound and is a clear thinker."
Wieland and pitcher Robbie Erlin were obtained from the Rangers in the July 31 trade last year that saw the Padres trade reliever Mike Adams to Texas.