The agency beat Archibald Ingall Stretton and Abbott Mead Vickers BBDO to the account. The incumbent, EHS Brann, did not repitch.
Draft will develop integrated activity to boost the charity's fundraising efforts.
Charities such as Oxfam are being forced to rethink their fundraising methods amid increasing pressure on the public to donate to disaster appeals such as those for the Asian tsunami and the Pakistani earthquake. Draft will look to recruit donors and campaigners using alternative methods such as DRTV.
Julia McKechnie, the corporate communications director at Oxfam, said: "Draft demonstrated understanding of the opportunities and challenges we face and presented strong creative ideas. We look forward to working with them."
EHS Brann split with Oxfam earlier this year amid internal disagreements within Oxfam about the future direction of the charity's fundraising efforts.