The brothers, Adi and Rudolf Dassler, began making sports shoes at home in the 1920s but fell out during the Second World War. The brothers set up their factories either side of a river in the Bavarian town on Herzogenaurach.
On Monday, employees of the two sports giants will shake hand and play a football match.
The match will be the first in a series of joint programmes between the sports giants which are no longer owned by any descendants of the brothers.
Puma, whose most prized ambassador is Usain Bolt, is owned by French luxury goods maker PPR. Adidas, which counts David Beckham, Kaka and Frank Lampard among its ambassadors, has numerous owners, none of which have more than 5% share.