Yang, who was born the son of a mathematics professor at Hefei in China, graduated from the National Southwest Associated University in Kunming and received an MSc from Tsinghua. A fellowship enabled him to travel to America, where he studied for his PhD at the University of Chicago, under Enrico Fermi. After teaching at Chicago he joined the Institute for Advanced Study, Princeton, becoming professor of physics in 1955. In 1965 he was appointed Einstein Professor of Physics and director of the Institute of Theoretical Physics at the State University of New York, Stony Brook.

Yang collaborated with Tsung Dao Lee, and in 1956 they made a fundamental theoretical breakthrough in predicting that the law of conservation of parity would break down in the so-called weak interactions. Their startling prediction was quickly confirmed experimentally, by Chien-Shiung Wu, and in 1957 Yang and Lee were awarded the Nobel Prize for physics.

Yang has also made other advances in theoretical physics. In collaboration with R. L. Mills he proposed a non-Abelian gauge theory – also known as the Yang–Mills theory – a mathematical principle describing fundamental interactions for elementary particles and fields. Yang has also made contributions to statistical mechanics.