Pridham, 52, spent 12 years with the Toronto Maple Leafs, most recently as the assistant general manager from 2018-26, working for many years under current Penguins GM Kyle Dubas.
Pridham and the Maple Leafs parted ways in May, as the team reshaped its front office under new general manager John Chayka.
Before his time in Toronto, Pridham spent 15 years with the NHL as a senior director of the Central Registry and a senior advisor of Central Scouting.
With the Maple Leafs, Pridham played an important role in helping to organize the salary cap around a core that included Auston Matthews, Mitch Marner, William Nylander and John Tavares.
He now heads to Pittsburgh, where he will help former Maple Leafs GM Dubas oversee player contract negotiations, salary cap management and scheduling.