Russell joins Aston Martin's Sebastian Vettel, chairman Alex Wurz and legal counsel Anastasia Fowle on the four-person panel that oversees the interests of all the drivers on the grid, particularly in the area of safety.
“It is an honour and privilege to be nominated director of the GPDA," said Russell.
"I appreciate the support of my fellow drivers in entrusting this role to me and recognise the responsibility it entails.
"In its six decades of existence, the GPDA has been an integral part of supporting and shaping F1 safety, for the sport and our fans.
"I am looking forward to tackling the new challenges and opportunities alongside Anastasia, Sebastian and Alex.”
Former Haas driver Grosjean had been a GPDA member for a number of years but has been forced to step down as a director following his departure from F1 at the end of last season and forging a new motorsport career in IndyCar.
The Frenchman, however, is to continue in the capacity as an advisor, notably as work continues in the area of safety following his fireball crash in last year's Bahrain Grand Prix.