Anna Elbina Morpurgo was born in Milan, the fourth child of a Jewish family. Her grandfather, Guido Castelnuovo, was a mathematician; her father, Augusto Morpurgo, was dismissed in 1938 under the Fascist racial laws and died the following year after trying to find a way to take his family to Argentina. She and her mother moved to Rome, where they survived with false papers and in hiding.
After the war, she earned her doctorate in classics from the University of Rome with a thesis on Linear B; she published the first lexicon of the language.
In 1961 she became a post-doctoral fellow at Harvard University's Center for Hellenic Studies in Rome, where she formed a deep interest in theoretical linguistics; she was later to help establish a chair in the subject at Oxford University. She moved to Oxford in 1962, became a lecturer in Classical Philology in 1964, and spent the remainder of her career there with the exception of guest teaching at various institutions in the United States.
In 1966 Morpurgo Davies became a fellow of St Hilda’s College; in 1971 she was appointed to the Chair in Comparative Philology and became a fellow of Somerville. In 2003 this became the Diebold Chair. She was also a Delegate of the Oxford University Press from 1992 to 2004, when she retired.
Morpurgo Davies published in many areas of Indo-European grammar. She was particularly known as an expert in the Anatolian languages, and was one of the decipherers of Luwian hieroglyphs. She was also known for her work on Mycenaean Greek and on the development of linguistics in the nineteenth century; in 1996 she published an Italian-language history of the latter, La linguistica dell'Ottocento, and in 1998 she was responsible for the volume on that century in the Longman History of Linguistics, where a reviewer found she set aside the overall editorial aim of tracing the development of linguistic thought in favour of presenting a history of the development of Indo-European linguistics in Europe and the United States.
In 2005 a reviewer at The Times referred to her "trend-setting work in onomastics, Greek dialectology, Mycenaean lexicography, Anatolian languages, writing systems, history of scholarship and social history".
Davies was made a fellow of the Society of Antiquaries of London in 1974 and of the British Academy in 1985. She was an honorary or corresponding member of the American Academy of Arts and Sciences, the Austrian Academy of Sciences, the Linguistic Society of America, the Academia Europaea, the American Philosophical Society, the French Académie des Inscriptions et Belles-Lettres, the Bavarian Academy of Sciences and Humanities, and the Italian Accademia dei Lincei. She became an honorary fellow of St Hilda's College in 1972 and was awarded honorary doctorates by the University of St Andrews and the University of Nancy.
In 2001, she became an honorary Dame Commander of the Order of the British Empire; since she retained Italian nationality, she could only use the post-nominals DBE.
In 2005 a festschrift was published in her honour, Indo-European Perspectives: Studies in Honour of Anna Morpurgo Davies.
She was married from 1962 to 1978 to the historian John K. Davies.