The French architecture practice has won the competition to overhaul the stadium in Clamart, which backs onto the Meudon Forest in the Parisian suburbs, in a bid to be used during the games.
"[The stadium] should be finished in 2024 and will surely be among the facilities for the Olympic Games in Paris," said a statement from the practice.
"The challenge of the restructuring and expansion of the Clamart stadium is to successfully reconcile the construction of a multiple and complex program with the tacit requirements of a place which, at the edge of the forest, almost calls for a place of reflection," continued the architect's statement.
Clamart's stadium sits in a natural hollow, so the architect has chosen to sink most of the facilities, including the gymnasium, athletics hall, bowling alley, games room into the side of the hill. A car park will be buried under the sports pitches.
Large skylights made from mirrored glass will puncture the living facade, allowing light into the areas below while reflecting the sky and the forest.
At night when the lights are turned on the mirroring process will reverse, reflecting beams back into the stadium.
The planted roofs and sides of the stadium will appear to blend with the forest behind it, and with a third of the stadium located underground the impact of the new building will be minimised.
The £36 million project is due to complete in 2024, in time for the Summer Olympics which will be held in the city that year.
The French firm has form when it comes to stadiums. For the UEFA Euro 2016 championship it overhauled a football stadium in Marseilles, adding an undulating ring-shaped roof.
SCAU are also building the £50 million Stade de Yamoussoukro in Ivory Coast for the 2021 Africa Nations Cup.