Wee joined UOB in 1979 and has been an executive director at the bank since 1990. He served as the deputy chairman and president from 2000 to 2007 and was appointed CEO in 2007 when his father Wee Cho Yaw, chairman of the bank, passed on the leadership to him. He is the current chairman of The Association of Banks in Singapore and also serves as a director of the Institute of Banking and Finance, council member of Singapore Chinese Chamber of Commerce and Industry and a director of several UOB subsidiaries and affiliates.