Westpac CEO Brian Hartzer said the rising cost of compliance had collided with lower fee revenue in the aftermath of developments such as the Future of Financial Advice reforms and the Hayne royal commission, forcing the bank to exit the business.
Mr Cooper said the many thousands of customers who Westpac provided advice to in the past would be referred outside the group "in much the same way they would if they needed an accountant or a lawyer".
Viridian is a boutique financial advice business that was formed by ex-Westpac employees with a staff of 130.
The private wealth, investment and superannuation platforms will be rolled into the business banking division, which will be run by Alastair Welsh in an acting capacity.
Mr Hartzer said bank hoped to complete repaying customers of employed advisers for fees-for-no-service by October and would update the market on its progress with aligned advisers in due course.