Yau was born in Shantou, Guangdong Province, China with an ancestry in Jiaoling (also in Guangdong) in a family of eight children. When he was only a few months old, his family emigrated to Hong Kong, where they lived first in Yuen Long and then 5 years later in Shatin. When Yau was fourteen, his father Chiou Chenying, a philosophy professor, died.
Since 1987, he has been at Harvard University, where he has had numerous Ph.D. students. He is also involved in the activities of research institutes in Hong Kong and China. He takes an interest in the state of K-12 mathematics education in China, and his criticisms of the Chinese education system, corruption in the academic world in China, and the quality of mathematical research and education, have been widely publicized.