Ridley is to be replaced by Bryan Sanderson, former chairman of Standard Chartered Plc.
Bank sources said Ridley's resignation would take effect as soon as Sanderson is approved as his successor by Britain's Financial Services Authority.
A spokesman said the process of appointing Sanderson had been in place since before Ridley underwent a three-hour cross-examination of Northern Rock directors by legislators on Tuesday.
During the session, Michael Fallon, a member of parliament for the opposition Conservative party, asked Ridley: "Does no one have any honour? Has no one offered to resign?"
Ridley responded: "I have made it clear that my resignation is available as soon as it is decided it is in the best interest of shareholders and stakeholders that I go."
Adam Applegarth, Northern Rock chief executive, and the rest of the board had also offered to resign.
Ian Gibson, senior non-executive director at the bank, said investors and advisors wanted the board to stay on to steer the bank through its crisis.
Northern Rock shares fell by over 30 per cent in September after it said it faced severe difficulties raising cash to cover its liabilities amid the ongoing global credit squeeze.
Northern Rock's management has been criticised since the Bank of England stepped in as "lender of last resort" on September 14.
The Newcastle-based lender has borrowed an estimated $32 billion from the Bank of England in the last five weeks.
Northern Rock has until February to assess its future options, including a possible sale.
It has received approaches from several groups, including a consortium led by the Virgin Group.