EHS triumphed in a final shootout against the incumbent, WWAV Rapp Collins, M&C Saatchi's Lida agency and Archibald Ingall Stretton. The review was handled by Agency Insight.
The win will plug the charity gap in EHS Brann's client portfolio, which was left when Barnardo's moved its direct marketing account into Partners Andrews Aldridge earlier this year without a pitch.
Oxfam kicked off the review in March after 11 years with WWAV.
Work that WWAV has created for Oxfam in the past includes its debut DRTV commercial featuring a man out fishing to provide food for his family.
The spot aimed to encourage regular donations to the charity by emphasising how much it promotes self-sufficiency among Third-World countries and was resurrected in January. The ad ran on national TV.
More recent work includes a mailing to 60,000 existing supporters to highlight the work it has carried out in response to international emergencies.
EHS will be charged with creating all direct marketing work from direct mail through to DRTV.
The review followed a series of management changes at the charity. Last summer, the former marketing director of the charity World Vision, Edward Fox, was appointed as the director of fundraising.
Then in April, the Oxfam marketing director, John Whitaker, left his job after 12 years with the charity.
WWAV also lost part of the Cancer Research UK account to Ogilvy & Mather.
However, it recently won Plan UK's £3 million direct marketing account.