He was born Alexander John Sharpe in Hoxton, Middlesex to a wealthy family. His father James Birch Sharpe was a notable artist and physician, who was later appointed Esquire of Windlesham. His mother Ann Ellis was from a noble background, but it is not known how her family made its fortune. Alexander's brother James Birch Sharpe junior, died at the Battle of Inkerman, during the Crimean War. His other brother William Henry Sharpe served with the Lancashire Fusiliers after moving north with his family to Cumberland, due to military work.
Alexander was educated at Shrewsbury School, Eton College and Trinity College, Cambridge (BA 1837). Initially trained in mathematics and the classics, he became a well-known phonetician of his time and wrote the article on phonetics for Encyclopaedia Britannica in 1887. Through his work in phonetics, he also became interested in vocal pitch and by extension, in musical pitch as well as speech and song.
Ellis is noted for translating and extensively annotating Hermann von Helmholtz's On the Sensations of Tone. The second edition of this translation, published in 1885, contains an appendix which summarises Ellis' own work on related matters.
In his writings on musical pitch and scales, Ellis elaborates his notion and notation of cents for musical intervals. This concept became especially influential in Comparative musicology, a predecessor of ethnomusicology. Analyzing the scales (tone systems) of various European musical traditions, Ellis also showed that the diversity of tone systems cannot be explained by a single physical law, as had been argued by earlier scholars.
In part V of his work On Early English Pronunciation, he applied the Dialect Test across Britain. He distinguished forty-two different dialects in England and the Scottish Lowlands. This was one of the first works to apply phonetics to English speech. The work was criticised by Joseph Wright, author of the English Dialect Dictionary, and Eugen Dieth, one of the pioneers of the Survey of English Dialects, but regained popularity in the second half of the 20th century as many dialect researchers said that their results were similar to that found in Ellis's work. Some have argued that much of Ellis's information was appropriated without sufficient citation by his critic Joseph Wright.