Richardson, the son of a woollen manufacturer from Dewsbury in the north of England, was educated at Cambridge University and at London University, where he became a DSc in 1904. He taught at Princeton in America from 1906 to 1913, when he returned to England to become Wheatstone Professor of Physics at King's College, London, where he remained until his retirement in 1944.

Richardson is noted for his work on the emission of electrons from hot surfaces – the phenomenon first observed by Thomas Edison and used by Edison, John Fleming, Lee de Forest, and others in electron tubes. Richardson proposed an explanation of what he named ‘thermionic emission’, suggesting that the electrons came from within the solid and were able to escape provided that they had enough kinetic energy to overcome an energy barrier at the surface – the work function of the solid. Thus thermionic emission of electrons is analogous to evaporation from a liquid. The Richardson law (1901) relates the electron current to the temperature, and shows that it increases exponentially with increasing emitter temperature.

Richardson published an account of his extensive work on thermionic emission in his book The Emission of Electricity from Hot Bodies (1910). His work was important for the development of electron tubes used in electronic devices, and he was awarded the 1928 Nobel Prize for physics for this work. During World War II he worked on radar.