The restricted free agent forward had a hearing scheduled for Aug. 23.
Aston-Reese, who will turn 27 on Aug. 10, scored 15 points (nine goals, six assists) in 45 games for the Penguins last season and two points (one goal, one assist) in six Stanley Cup Playoff games.
"Zach is a versatile forward that brings energy and edge to our lineup," Penguins general manager Ron Hextall said. "He is a responsible, two-way player and we're glad we were able to re-sign him."
Signed by Pittsburgh as a free agent March 14, 2017, Aston-Reese has scored 51 points (27 goals, 24 assists) in 161 regular-season games and four points (one goal, three assists) in 23 playoff games.