Reporting to ASOS chief executive Nick Robertson, Dobbie, who takes up her post in March, will also be a member of the ASOS.com operating board.
ASOS has just appointed Mother without a pitch as its first advertising agency of record.
Prior to consulting for Mother Dobbie was the initial vice-president of marketing for Europe at Gap and was responsible for setting up the European marketing team and launching Banana Republic in London.
Dobbie started her career in advertising and worked on a variety of brands, including Nike, at the creative agency Simons Palmer - now part of TBWA - before leaving to spend four years as the marketing communications director at Nike UK, overseeing the successful launch of Niketown. She later joined French Connection as marketing director.
She joins at a buoyant time for the online fashion retailer that has 1.5 million active customers. It experienced substantial growth in the run-up to the recent festive period, with sales increasing 30% year on year over the Christmas period. Sales year on year for the 42 weeks to 17 January have risen 38%, with UK sales up 25% and international sales up 102% year on year.