Among the 16 Clydesdale branches to be axed is one in Glasgow's Govanhill.
Six "flagship" branches will be developed - including a Clydesdale Bank in Glasgow - as well as improved mobile and internet banking services under a programme to "replace, renew, relocate and reinvest" across the retail branch network.
Clydesdale and Yorkshire, part of National Australia Bank, said it will save £5m by the branch closures, adding that frontline jobs will be safeguarded.
New posts are being created at the banks' busiest branches, while support will be given to displaced branch managers.
David Thorburn, chief executive of Clydesdale Bank and Yorkshire Bank, said: "There's a lot of positive change being driven forward for our customers and there needs to be more as we build a better bank. Here we are making a significant investment to meet the changing needs of customers now and in the future.
"But to deliver what are fundamentally necessary changes, we have to face in to difficult decisions. No branch closure is welcomed by customers or staff, I understand that, which is why we are working to minimise the effects these changes have on them."
Unite union national officer Rob Macgregor said: "The bank is cutting costs and eroding community banking which we believe leaves customers with less choice.
"Customers are being short-changed by high street banks replacing counter staff with machines, yet, according to our own poll, nearly three-quarters of people want the human touch, not just a machine in their local bank branch.
"Unite will oppose compulsory redundancies and we expect the company to do everything possible to make redeployment an option and allow workers to move to neighbouring branches wherever possible."