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.