Hudson, who threw a bullpen session Tuesday, felt his shoulder held up well Wednesday and he will next throw a simulated game later this week.
If that goes well, he'll move on to a live game, throwing 50 pitches followed by another live game with 75 pitches with bullpen sessions in between each outing.
D-backs manager Kirk Gibson said the club hasn't decided where Hudson will throw his rehab starts yet, whether in extended spring training or in the Minor League system.
Young will play Thursday at Salt River Fields in an extended spring training game. The team wants him to get as many at-bats as possible.
Drew will also play Thursday in the same game with Young and then again on Saturday.
"They're going to have a pretty good team over there," Gibson quipped.