The 24-year-old forward recorded eight goals and 17 points for the Penguins last season while being limited to 43 games due to a broken hand.
"Zach is a responsible player who plays a solid two-way game," said Penguins general manager Jim Rutherford. "He has a heavy style of play that is especially effective on the forecheck and penalty kill."
After being named a finalist for the Hobey Baker Award due to his dominance at the collegiate level with Northeastern University, Aston-Reese signed a two-year, entry-level contract with Pittsburgh ahead of the 2017-18 season.
The Penguins are now $157,000 above the cap ceiling of $81.5 million with a full 23-man roster, according to CapFriendly. However, teams can exceed the cap by 10 percent during the offseason. The Vegas Golden Knights and New York Rangers are the only other teams currently above the ceiling.