Simpson was born on 8 February 1875 in Glasgow, Scotland, and went as a young man to New York City, where he worked for four decades on Broadway from 1906 until his death.

In 1929 he portrayed Hugh Myers in Disraeli, where he played along his close friend George Arliss.

He often played servants, like in MGM's literature adaption David Copperfield as Littimer and the horror movie Mark of the Vampire.

He also portrayed priests like in Little Lord Fauntleroy and Random Harvest, judges like in This Land Is Mine or doctors like in They All Kissed the Bride.

Simpson was also a frequent actor in the Errol Flynn movies, he appeared in The Adventures of Robin Hood, The Prince and the Pauper and Captain Blood.