VCCP beat two other agencies in the final stages of the contest, which was run in-house.
Asos has worked with Bartle Bogle Hegarty on global digital campaigns and, before that, appointed Mother as its first advertising agency in the UK in 2010.
Carat was the incumbent media agency in the UK, but resigned the account this year.
Nick Robertson, the chief executive of Asos, said at the beginning of the year that he wanted the company to "redeploy spend more effectively" after doubling its marketing budget to £40 million in 2013.
Asos reported a 14 per cent fall in pre-tax profit to £46.9 million for the 2013/14 financial year.
The company attributed the loss of tens of millions of pounds in sales to a fire in June that destroyed its distribution centre in Barnsley. However, it still reported sales growth of 35 per cent in the UK, 19 per cent in the US and 44 per cent in mainland Europe.