As an English name it was not used until after the Protestant Reformation. It was utilized by George Eliot for the title character in her novel Silas Marner (1861).
A notable bearer was the American musician Miles Davis (1926-1991). In Scotland this name was historically used to Anglicize Maoilios.
As a rarer (but older) masculine name it is probably derived from a surname: see Fay 1 or Fay 2.
Because Elijah was a popular figure in medieval tales, and because his name was borne by a few early saints (who are usually known by the Latin form Elias), the name came into general use during the Middle Ages. In medieval England it was usually spelled Elis. It died out there by the 16th century, but it was revived by the Puritans in the form Elijah after the Protestant Reformation. The name became popular during the 1990s and 2000s, especially in America where it broke into the top ten in 2016.
It has only been commonly used as a given name since the 20th century, influenced by two plays featuring the character: William Butler Yeats' Deirdre (1907) and J. M. Synge's Deirdre of the Sorrows (1910).