It scooped the business after seeing off competition from M&C Saatchi and three other undisclosed agencies.
The agency will now be charged with developing a brand positioning to raise Dunhill's profile across a number of key countries, including the UK, Asia, Japan and the US.
Adrian Coleman, a VCCP partner, said: "Alfred Dunhill is an iconic brand that deserves iconic advertising. We are looking forward to the challenge."
The agency is expected to produce a poster, press and direct marketing campaign. Their first work is scheduled to roll out in the autumn and is likely to be a tactical ad.
Paddy Byng, the marketing director at Alfred Dunhill, who oversaw the pitch process, said: "Dunhill is continuing to launch new and innovative products across all men's accessories categories and will be working with VCCP to develop compelling advertising in support of our product strategy."
The brand, which currently creates its ads in-house, is owned by the Swiss luxury goods group Richemont.
The creative appointment does not affect Media-edge:cia, which handles the media across Richemont's portfolio of brands.
Other brands in the stable include Cartier, Jaeger and the upmarket men's fashion retailer Hackett.