The 24-year-old Young went a combined 2-5 with a 2.88 ERA at two levels of Class A ball in 2008, his fifth professional season.
The Padres and Mets each made two picks during the major league phase of the draft. San Diego selected shortstop Everth Cabrera third overall from Colorado and right-hander Ivan Nova at No. 20 from the New York Yankees.
The Mets, seeking more help for their revamped bullpen, chose relievers Darren O'Day from the Los Angeles Angels and Rocky Cherry from Baltimore.
"We'll bring 'em into camp and see what happens," Mets general manager Omar Minaya said. "Gives us flexibility."
Players chosen in the Rule 5 draft must stay on the active major league roster with their new club all season or be offered back to their old team for $25,000.
Current major league stars who were Rule 5 picks include Johan Santana, Josh Hamilton and Shane Victorino.
There were 21 selections made during the major league phase. The Yankees had four players poached from their Triple-A roster while the Angels lost three.
The Kansas City Royals chose left-hander Jose Lugo ninth overall and then traded him to the Seattle Mariners for cash.
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