Milone will face the Mets on Thursday afternoon, and Lannan will face the Marlins at Nationals Park on Friday.
Peacock threw a bullpen session on Friday, and another one on Sunday.
"I'm excited," Peacock said about making his first Major League start.
Peacock last pitched on Tuesday, the same day that Stephen Strasburg made his season debut. Peacock pitched 1 1/3 innings, allowing a run on four hits in a 7-3 loss to the Dodgers.
"That was unfair to begin with," manager Davey Johnson said about Peacock pitching in relief. "I think we are going to have a start [for him] in about three or four days."
Peacock went a combined 15-3 with a 2.39 ERA and 177 strikeouts in 25 games with Triple-A Syracuse and Double-A Harrisburg this season. The 23-year-old ranked high among all Minor League pitchers in wins (tied for second), strikeouts per nine innings (sixth, 10.86) and strikeouts (seventh).