The banks will be floated under the name CYBG and NAB has said it will release more information on its plans in the week beginning 7 December.
NAB has said it will seek to spin off about 75 per cent of Clydesdale and Yorkshire banks to shareholders and sell the rest to institutional investors through an IPO planned for February.
A statement issued to the London Stock Exchange said: “The National Australia Bank board today formally decided to proceed with the demerger and proposed IPO to institutional investors of CYBG Plc.
“The proposed demerger and IPO remain subject to a range of matters, including various court and regulatory approvals and NAB shareholder approval.”
NAB has owned Clydesdale Bank since 1987 and Yorkshire Bank since 1990.
In May NAB said it was looking into offloading the two subsidiaries, adding that it was instructed by the PRA to set aside a further £1.7bn for potential redress.