HMDG will be responsible for the advertising for an Adidas product launch next year. Activity will run globally across online, point-of-sale and outdoor.
Earlier this year, Adidas introduced a special edition of the male fragrance Pure Game, to celebrate the football fans and participants of this summer's World Cup.
Since its partnership with Coty in 1985, the brand has become a leader in the male fragrance market and is distributed across 82 countries.
In July, Coty hired JWT UK to handle the global digital advertising for Rimmel London after a three-way pitch.
The HMDG founder Nick Hurrell said: "Coty is a creative, commercial and hugely influential business working with many of the world's best-known brands. We are delighted to have joined its roster of agencies."