Hudson, who had back surgery last November, will make his 2012 debut on Sunday against the Pirates, with Minor starting the series finale on Monday night.
"We were prepared to go the other way if Huddy needed it," Braves manager Fredi Gonzalez said. "But this way, he goes with his regular turn."
"I'm ready to go," Hudson said. "No problems at all."
Hudson made four Minor League starts, the final two with Triple-A Gwinnett. He was 2-0 with a 0.84 ERA for the G-Braves, working five innings in the first game and 5 2/3 innings in the second.
"I'm happy with it," Hudson said after his final tuneup. "I felt a little more crisp. I felt like my sinker was pretty good, some really good curveballs. It was a sign of getting some touch back with my off-speed pitches."
Best of all, Hudson has had no back discomfort.
"Back feels great. It's not an issue," Hudson said. "My legs are feeling pretty good. I feel like they're getting under me. My arm strength is gradually getting a little better."
Hudson's fastball was sitting at 91 mph during his final rehab start, with one pitch reaching 92 mph.
"I feel like my velocity was better than it was in my other starts," he said. "Consistently, I feel like it's staying where I want it."
Minor, 2-1 with a 3.42 ERA, threw 79 pitches over six innings in a no-decision against the Dodgers on Tuesday. He allowed eight hits and three runs.