The announcement came after the well-known music chain stopped accepting vouchers as payment for its products, despite issuing them until the day before it went into administration.
The administrators also said they would forward all proceeds made from charity releases including the Hillsborough Justice Collective single as soon as possible.
Nick Edwards, Joint Administrator said the decision to honour gift cards had been made after assessing HMV's financial position.
"We recognise that both of these matters have caused concern for individuals and organisations affected and are pleased to have reached a positive outcome," he said.
"We will continue to assess the longer term options for the business whilst continuing to trade. I am hopeful this process will result in the business continuing as a going concern."
There are eleven stores in the region, five of which are based in Belfast.
A Deloitte spokesperson said that gift cards would be honoured across stores in Northern Ireland.
The music chain was established 92 years ago and operates 238 outlets across the UK, employing more than 4,000 people.
It called in the administrator after poor sales over Christmas meant it could not meet its financial commitments.
Gift cards are not being accepted by HMV in the Republic and its shops remain closed.
Deloitte is attempting to find a buyer for the 16 stores as the company is in receivership there.
Sit-ins at several of the Irish shops ended on Saturday after workers were promised they would receive their wages.
Music giants including Universal, Warner and Sony are reportedly offering incentives including generous credit terms and discounted CDs and DVDs to any potential buyer for the company in the UK.