Greenberg will be the fifth person to receive the award, which recognises "a person whose devotion and vision has helped shape the way forward for the industry", according to Terry Savage, chairman of the festival.
Other recipients include the director Joe Pytka, Sir John Hegarty, Dan Wieden and Lee Clow.
Greenberg will receive the gong during the awards ceremony on 27 June. Over the years, R/GA has won almost 60 Lions at the festival, according to its organisers, making it one of the most successful integrated marketing services agencies.
Savage said: "[Greenberg] is a man that reinvents his agency business model every nine years to ensure that they are in line with technology shifts.
"He’s created ground-breaking visual effects and is behind the Titanium Grand Prix winning Nike+ Fuelband campaigns. It’s an honour to be able to celebrate Bob’s talent and unstoppable drive."
Greenberg said: "Throughout my career, and every incarnation of R/GA, I have always strived to ensure that creativity remained at the heart of everything we did.
"I am honoured that the Cannes Lions Festival feels that my efforts are worthy of this prestigious award and have included me among such distinguished company."