The agency won the business after a review process, which also involved the previous incumbent, DTV Group.
Albion will be responsible for handling Wonga's advertising activity, as well as its digital, direct marketing and social media work.
Last year, Wonga spent around £4 million on advertising in the UK. However, it is expected to more than double that amount this year.
A heavy user of TV advertising, Wonga also sponsors Blackpool FC and partnered with Transport for London to sponsor free Tube travel last New Year's Eve.
Last July, Wonga's TV ads came under fire from the Advertising Standards Authority for "trivialising" the high interest rates applied to short-term loans.
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