The fashion website was forced to suspend orders after the blaze on Friday night hit 20 per cent of stock at the site. The firm said the stock had been compromised by either fire damage or the sprinkler systems
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 on Monday.
The company said it is fully insured for the loss of stock and the interruption to business.
It added that none of the technology, automation or structure of the building has been affected by the fire.
At the end of May, Asos held £159m of stock at cost, of which around 70 per cent is held at Barnsley.
The fire is the latest blow to the firm after it issued its second profits warning in three months earlier this month, saying that the strength of the pound had hit overseas sales.