The son of a minister of the Free Church of Scotland, Ewing was educated at the University of Edinburgh where he studied engineering. He served as professor of engineering at the Imperial University, Tokyo, from 1878 until 1883 when he returned to Scotland to a similar post at the University of Dundee. In 1890 he was appointed professor of applied mechanics at Cambridge University, but in 1903 moved into higher levels of administration, first as director of naval education and from 1916 until his retirement in 1929 as principal and vice-chancellor of Edinburgh University.

In Japan he worked on problems in seismology and in 1883 published Treatise on Earthquake Measurement. However, his most notable achievement as a physicist was his work on hysteresis, first described by him in 1881. Hysteresis is an effect in which there are two properties, M and N, such that cyclic changes of N cause cyclic variations of M. If the changes of M lag behind those of N, there is hysteresis in the relation of M to N. Ewing came across the phenomena when working on the effects of stress on the thermoelectric properties of a wire. Hysteresis effects were later shown to apply to many aspects of the behavior of materials, in particular in magnetization.

Ewing was put in charge of the cryptologists at the Admiralty from 1914 to 1916. He described his work there in his book The Man in Room 40 (1939).