Alexander George Ellis was born on 14 October 1858, son of Frederick Charles Ellis, of the Paymaster General's Office, Whitehall. He was the last in a direct family line of public servants, whose lives, incidentally, each approached or exceeded the span of ninety years. His great grandfather, a Doctor of Divinity, came to London from his native Yorkshire well back in the eighteenth century. His grandfather, Sir Henry Ellis directed the British Museum from 1827 to 1856, and it is perhaps not surprising that A. G. joined the staff of the Museum in 1883 and spent the next twenty-six years there, chiefly in cataloguing Islamic literature, at first printed books and later both books and manuscripts.

Ellis was educated at the Merchant Taylors’ School, where he was solidly grounded in Hebrew as well as in the classics, and went on to Queens’ College, Cambridge, where he matriculated as a Pensioner in Michaelmas Term 1877 and studied at the feet of William Wright and other eminent Orientalists. He became a Scholar in 1878 and a recipient of the Tyrwhitt Hebrew Scholarship upon graduating with a first-class degree in Semitic Languages in 1881. He left Cambridge with a sound equipment in Hebrew, Syriac and Arabic, and he soon extended his studies to include Persian, Turkish and Armenian, which enabled his work to cover an unusually wide field.

In 1894 he published volume one of his Catalogue of Arabic Books in the British Museum, the second volume appearing in 1901. This meticulous work of reference contains descriptions of nearly all the printed Arabic literature acquired by the Museum during the nineteenth century. For his first ten years at the Museum Ellis had as a senior colleague Charles Rieu, author of the monumental catalogues of Arabic, Persian and Turkish manuscripts, and after Rieu's retirement Ellis became to a large extent responsible for dealing with the Islamic manuscripts acquired by the Museum, as well as the books. Part of his work in this field was published together with Edward Edwards. He was also joint author of the Supplementary Catalogue published in 1926.