The bank announced the closures on Wednesday, saying an ongoing decline in branch usage had led to the decision.
Saltcoats, Troon, Beith and Cumnock branches will close in the coming weeks.
A statement read: "This ongoing decline in branch usage, married to a sharp and sustained increase in digital and mobile engagement, has driven a shift to providing greater access to day-to-day banking services remotely, on the move and outside of normal business hours.
"The bank continues to reshape its service offering in response to these changing needs.
"To support this transformation the bank is committing £350m over the next two years, embracing digital innovation while continuing to invest in a more sustainable branch network to deliver a superior customer experience."
The bank said it would try to find roles for frontline branch staff either within other branches or elsewhere in the bank wherever possible.
However, it added: "However, there will inevitably be employee number reductions as a result of these changes.
"All employees affected by these changes will be fully supported through the process."
Unite the union said it was "bitterly disappointed" by the move, which will also see 39 branches close south of the border with another 200 job losses.
Rob MacGregor, Unite national officer, said: "Staff across the Clydesdale and Yorkshire Bank will be devastated to learn that 79 branches will close and consequently over 400 colleagues will lose their jobs.
"Unite is clear that the closure of a third of the bank's branches will not only be concerning for staff but the local communities which will see their bank branch close. This cost cutting plan leaves customers with less choice for local banking.
"Unite workplace representatives will be able to assist members over the coming days and weeks to support staff impacted by this announcement."
The branches set for closure include: Aberdeen Riverside, Aberlour, Aboyne, Alloa, Banff, Bathgate, Bearsden, Beith, Bellshill, Brechin, Buckie, Cambuslang, Castle Douglas, Cumnock, Dalkeith, Dunoon, East Kilbride Stuart Street, Edinburgh Leith Walk, Edinburgh University, Forfar, Fraserburgh, Giffnock, Glasgow Aikenhead Road, Glasgow Bath Street, Glasgow Charing Cross, Grangemouth, Johnstone, Leith, Leven, Mintlaw, Renfrew, Rosyth, Rothesay, Saltcoats, South Queensferry, Stonehaven, Stranraer, Thurso, Tillicoultry and Troon.
