Davis' cancerous thyroid gland was removed April 10. He was declared cancer-free this month and rejoined the Diamondbacks for this week's series at Florida.
"It really just feels like he never left, although you know what he's been through," Melvin said.
Davis, who has missed 36 games this season, made two rehab starts for Triple-A Tucson.
"He never really got in prolonged tired spells like we had been told he might," Melvin said. "Being the athlete that he is, he keeps himself in great shape and so forth. Obviously, that had something to do with it."
Davis' cancer was discovered before the season, but he made two starts before undergoing surgery April 10. He is 1-1 with a 3.72 ERA.
"He's a mainstay in our clubhouse and a guy that's very well-respected here," Melvin said. "We all felt for him for what's he's going through, but I think he's the type of guy that doesn't want to put any extra distractions on the team. He just wants to move on past this thing and go about his business."
Davis went 13-12 last year with a 4.25 ERA. Melvin declined to say how the Diamondbacks will free a roster spot for Davis.
"I'm just going to treat it like any other start," Davis said. "There's nothing special about it, really. It's just another start. I'll get out there and try to execute my game plan, and that's the bottom line."