Woo was born in Shanghai, China and moved to Hong Kong in 1949. He was educated at St Stephen's College, a Direct Subsidy Scheme privately owned but government-funded boarding school (which is also Hong Kong's largest secondary school), in the town of Stanley in Hong Kong, and went on to attain his bachelor's degree from the University of Cincinnati, US, majoring in Physics and Mathematics. While a student at the University of Cincinnati, Woo became a member of Delta Tau Delta Fraternity, an endeavour he is still involved in today. He later obtained an MBA from Columbia Business School in New York, US.
In 1973, he married Bessie Pao. In 1975, he joined his father-in-law, the late Sir Yue-Kong Pao’s Worldwide Shipping Group and was later appointed vice-chairman for the company. In 1986, Woo's father-in-law retired and appointed him the head of the Wheelock / Wharf businesses, while putting the shipping interests (now Bergesen Worldwide) under the control of another son-in-law, Helmut Sohmen.
The Hong Kong SAR Government appointed Woo Justice of the Peace in 1993, awarded the Gold Bauhinia Star in 1998 and the Grand Bauhinia Medal in 2012.
Woo is a member of the Standing Committee of the Chinese People’s Political Consultative Conference.