Born in Dundee, Scotland, the third son of a minister of the Free Church of Scotland and educated at West End Academy and the High School of Dundee, Ewing showed an early interest in science and technology.

Ewing won a scholarship to Edinburg University where he studied under William Thomson, 1st Baron Kelvin and Peter Guthrie Tait before graduating in engineering. During his summer vacations, he worked on telegraph cable laying expeditions, including one to Brazil, under Thomson and Fleeming Jenkin.

Japan
In 1878, on Fleeming Jenkin's recommendation, Ewing was recruited to help the modernisation of Meiji Era Japan as one of the o-yatoi gaikokujin (hired foreigners). Serving as professor of mechanical engineering at the University of Tokyo, he was instrumental in founding Japanese seismology.

Ewing made two special friends at Tokyo University soon after arriving: Basil Hall Chamberlain and Lieutenant Thomas Henry James R.N. who taught navigation. He was also in close contact with Henry Dyer and William Edward Ayrton at the Imperial College of Engineering (Kobu Dai Gakko).

In Tokyo, Ewing taught courses in mechanics and on heat engines to engineering students, and electricity and magnetism to students of physics. He carried out many research projects on magnetism and coined the word 'hysteresis'. His investigations into earthquakes led him to help T. Lomar Gray and John Milne of the Imperial College of Engineering to develop a seismometer. All three men worked as a team on the invention and use of seismographs, though Milne is generally credited with the invention of the first modern horizontal-pendulum seismograph.