The fashion website was forced to suspend orders after the blaze in Barnsley on Friday night affected 20% of stock at the site.
The fire is believed to have been started deliberately and is being investigated by South Yorkshire Police. Around 500 workers were evacuated from the five-storey building.
Asos said the clean-up process started on Saturday morning and meant it was able to resume taking orders at 2am today.
The company is fully insured for the loss of stock and business interruption, although the disruption meant its shares fell 3%.
Asos said in a stock market statement: "None of the technology, automation or structure of the building has been affected by the fire.
"Our initial estimate is that approximately 20% of the total stock at the site has been compromised by fire damage and the sprinkler systems."
At the end of May, Asos held £159 million of stock at cost, of which around 70% is held at Barnsley.
The retailer sells fashion and beauty products around the globe and last year made sales of more than £750 million.
The fire is the latest blow to the firm after it issued its second profits warning in three months earlier this month.
Shares slumped by as much as 40% - wiping £1.5 billion from its market value - after the company said the strength of the pound had hit overseas sales and forced it into a rash of promotions.