The central London store had been earmarked for closure in June, as part of a company voluntary arrangement the group entered into in a bid to cut costs, which had become “unsustainable”.
It was one of 31 branches, out of a total 59, set to shut down across the UK and Ireland, with up to 6,000 jobs at risk.
However, the department store was forced to call administrators in earlier this month after failing to reach a deal with creditors.
Mr Ashley’s purchase of the retailer for £90m was revealed just hours after the company collapse.
He vowed to keep 80 per cent of the store network open, and said he would introduce more luxury brands such as Gucci and Prada to the product line, in an effort to make House of Fraser the “Harrods of the High Street”.
James Keany of CBRE, the real estate firm which is advising House of Fraser on its property portfolio, said: "This deal only happened because all parties realised it was better to keep the store open and fully operational.
"It was a real case of landlord and tenant genuinely working together and at great speed."
Michael Murray, Sports Direct's head of elevation, said the speed with which the deal was struck showed a commitment to turn around the House of Fraser business.
He said: "We said we would keep as many stores open as possible, and in less than a week we have saved the biggest store.
"Oxford street was meant to close in January and now it's safe, which is great news for all parties.
"Everyone must remember it was a bust business and we need landlords, councils and brands to pull together to save House of Fraser on the high street."
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