The investigation was confirmed in a letter from Amyas Morse, head of the NAO, to the shadow financial secretary Chris Leslie.
Leslie had asked the public spending watchdog to delay the sale so it could pre-assess the deal.
Morse however said that the NAO could only investigate a completed sale and could not stop the deal going through.
Morse said: “I can confirm that I have decided to conduct a value-for-money study in relation to the creation and sale of Northern Rock plc.
“However, my role in conducting value for money studies is to act as an auditor, in this case of the completed sale transaction.”
Morse added that the probe would be carried out “as a matter of urgency”.
The sale of the state-owned bank is likely to mean a loss of between £400m and £650m and Labour is urging the government to delay the sale. However ministers insist they got taxpayers the “best possible deal”.
It argued it was the right time to sell because Northern Rock was predicted to remain loss-making well into 2012.
But Labour criticised the move saying the government should have sought an extension on an EU deadline which requires the bank to be sold by the end of 2013. Chancellor George Osborne has said the deadline was negotiated by his Labour predecessor Alistair Darling.
Taxpayers originally injected £1.4bn into Northern Rock in 2010, meaning at face value the sale represents a loss of £650m.
Leslie said: “There is clearly strong evidence to suggest that this Northern Rock fire sale represents poor value for money for the taxpayer.
“This investigation by the independent National Audit Office confirms that serious questions hang over George Osborne's deal.
“At present there is the possibility that those buying Northern Rock could asset-strip so much from the firm that they get back virtually every penny they invest within a matter of months.
“Ministers haven't thought through this deal carefully enough - they have a duty to do better than this."
