Mr Wuffli will be succeeded by the firm's deputy chief executive officer Marcel Rohner, who had been heading the group's wealth management division and overseeing assets of $2.5 trillion.
The former-CEO's departure follows the rejection of a proposal from UBS chairman Marcel Ospel that Mr Wuffli should succeed him.
As a result, Mr Ospel has agreed to remain in his position for another three years.
News of developments was foreshadowed by a drop in profit at the bank and the closure of its Dillon Read Capital Management at a cost of $300 million, as the company underperformed compared with its rivals.
This has led to calls from shareholders and critics that UBS should break up the company and extricate itself from investment banking to focus on investment and wealth management.