Heatherwick Studio will lead the overhaul of the Riverside stand at Craven Cottage, the club's west London home since 1896.
Heatherwick was personally chosen by Shahid Khan, the owner of Fulham Football Club, as part of a major investment to increase capacity at the ground.
"The Riverside Stand project required patience and diligence, and ultimately a designer who understands the history of London, the Thames and, of course, Fulham," said Khan. "Thomas Heatherwick is that designer."
He added: "I have had many meetings with Thomas in the past half-year and while his work speaks for itself, to hear him articulate his vision is something else. Thomas will bring to life what the project, the neighbourhood and the Fulham community deserve.”
The project is part of a wider project aimed at returning the club, which currently plays in the English Championship league, to the elite Premier League.
Situated beside the River Thames, Craven Cottage has a capacity of just 27,600 spectactors.
The Riverside stand is one of four stands at the ground, which were all built at different times to different designs. It is the most visible of the four, as it backs on to the river.
The club issued a statement saying it hoped that Heatherwick's appointment would enable Khan "to fulfil his aspiration of creating an iconic landmark on the banks of the River Thames."
Heatherwick's appointment follows news that Swiss architects Herzog & de Meuron are to redesign Stamford Bridge, the west London home of Chelsea FC.
The London-based designer, who came to international prominence with his design for the cauldron used at the London 2012 Olympic Games, has also redesigned the iconic red London bus and is working on the Garden Bridge, a proposed pedestrian crossing in Central London.