A spokesman for the Rock said the sale of the Irish subsidiary leaves it solely with a UK presence and will allow it focus its efforts on the UK.
The deadline for bids from potential purchasers of the Rock passed earlier this month and the bids are currently being scrutinised and assessed.
Virgin Money and US investment fund JC Flowers are believed to be the two front runners for the bank’s retail division which consists of 70 branches.
The Rock statement added: “The sale of NRI is not linked to the process for returning the company to the private sector, which is an entirely separate matter. As previously announced, UKFI, the company and advisers are exploring the option of a sale of Northern Rock plc.”
Sandler added: “We are delighted to have entered into an agreement with Permanent TSB and the sale is expected to complete by the end of the year.”
David Guinane, chief executive of Permanent TSB, said: “We are delighted to reach this agreement with Northern Rock to acquire their Irish savings business.
“This move represents another milestone in the growth of our savings business and we look forward to welcoming the 17,000 new customers to the bank in the coming months.”