The Glasgow-based bank, which also includes Yorkshire Bank, will float 70-80% of its shares to NAB shareholders and the rest to institutional investors.
NAB expects to complete the spin off by the end of 2015, while the deal is subject to approval from regulators and key stakeholders.
Andrew Thorburn, the NAB’s chief executive, said: “It is a priority to exit this business, and we are today announcing our intention to pursue a demerger and initial public offering of the UK banking business."
The Australian bank plans to raise £2.88bn in capital to boost its balance sheet ahead of anticipated regulation.
Debbie Crosbie, Clydesdale’s acting chief executive, said: “Today’s announcement marks the beginning of an exciting new opportunity for Clydesdale and Yorkshire Banks.
“Our performance is improving and we’re providing real customer choice in the UK which is driving encouraging growth across our target retail and SME markets.
“We believe the foundations of a strong standalone future have been laid in the progress made restructuring and refocusing our business and this is clear in our half year results.”
Clydesdale Bank increased its mortgage lending by 14.5% to £2.4bn in the six months to 31 March 2015, while it upped its pre-tax earnings by a third to £118m.
But the lender is commonly seen as a drag on NAB’s profits, as the lender was fined a record £20.7m in April for its treatment of customers seeking payment protection insurance payouts.