The agency won the account following a four-way pitch, handled by Oxfam, against undisclosed agencies.
Code Computerlove will work alongside Oxfam's digital, marketing and communications teams, providing strategic support and launching creative campaigns to raise funds and enable supporters to donate money.
The Charity has previously handled its digital work in-house, using agencies such as Razorfish on a project basis.
Sarah Jordan, Oxfam head of digital communications, said: "Digital communication has become vital in helping Oxfam to achieve its goals. In particular we aim to deliver greater supporter engagement and increase revenue through digital channels.
"Code demonstrated it had the passion, capabilities and breadth of offer to help us to achieve our digital vision and we will be calling on their unrivalled digital marketing and technical experience."