The leather goods, menswear and men's accessories company's marketing director Paddy Byng appointed the agency after a four-way pitch.
Snowball has been working with Alfred Dunhill in the UK since September 2003.
The global brief will see Snowball advising on the rollout of the customer segmentation, contact and acquisition initiatives it has developed for the domestic business.
Damian Bentley, managing director of Snowball, said: "We're very pleased to be appointed by Dunhill on a global basis. It is a great brand to work with and it is committed to using direct marketing in a very innovative way."
Snowball's clients include Bang & Olufsen, luxury bed manufacturer Duxiana, health spa The Chelsea Club, and West End celebrity haunt, No 5 Cavendish Square.
Richemont, which owns the Alfred Dunhill brand as well as Cartier and Hackett, is currently reviewing its media planning and buying arrangements with a view to consolidating them into a single global network.
The majority of the account is split between three networks: Mediaedge:cia holds the £70m account in Europe, Universal McCann is the incumbent in North and Latin America, while OMD holds the business in Asia.
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