He will be replaced at the top by Nick Beighton, the company's chief operating officer, with immediate effect. Beighton joined ASOS in 2009 as chief financial officer, stepping up to the COO role last October.
"I'd like to acknowledge Nick Robertson's extraordinary achievement. His passion and vision have built a start-up into a world class company," said ASOS chairman Brian McBride.
Until last year, when it issued three profit warnings due to currency swings and higher investment needs, ASOS, with Robertson the driving force, had been the success story of the British retail sector and a darling of the stock market.
Robertson and Quentin Griffiths founded the-then As Seen On Screen in 2000 and floated the firm on London's Alternative Investment Market at 20 pence in 2001.
The shares hit a high of 71.95 pounds in February 2014 before the first of the warnings. The stock closed at 29.84 pounds on Tuesday, valuing the business at 2.5 billion pounds ($3.83 billion).
ASOS had a tough 2014 when it was hurt by the negative impact of exchange rate movements and a fire at its main warehouse. However, its shares have risen 16 percent so far in 2015 as it has recovered. Last month it raised its full-year profit guidance after a strong third quarter.
Robertson owns 8.4 percent of its equity, according to Reuters data.
ASOS shares fell by up to 3.7 percent after the news was out on Wednesday.