The appointment is expected to lead to a new brand campaign which is likely to feature Jamaica's Olympic gold medal-winning sprinter Usain Bolt. Bolt's 100m world record at the Beijing Olympics helped raise Puma's profile.
Puma's shoes and clothing are sold in more than 120 countries around the world. The sportswear brand has used a number of agencies in the past and this is reported to be the first time it has appointed a lead agency.
Antonio Bertone, chief marketing officer at Puma, said: "One of the hallmarks of Puma is our ability to push the envelope, whether in product design or in the way we talk about our brand.
"As a company we are naturally drawn to agency partners who share our DNA: the small but mighty, the evolutionists, the challengers. Droga5 is just such a partner."
Droga5 was launched by Australian Dave Droga in 2006. Its clients including clothing brand Ecko, Pernod Ricard and Coca-Cola.