Diakonoff was brought up in Norway. He graduated from Leningrad State University (now Saint Petersburg State University) in 1938. In the same year he joined the staff of the Hermitage Museum in Leningrad (now Saint Petersburg). In 1949 he published a comprehensive study of Assyria, followed in 1956 by a monograph on Media. Later on, he teamed up with the linguist Sergei Starostin to produce authoritative studies of the Caucasian, Afroasiatic, and Hurro-Urartian languages.
Diakonoff was honored in 2003 with a volume published in his memory, edited by Lionel Bender, Gábor Takács, and David Appleyard. In addition to articles on Afro-Asiatic languages, it contains a five-page list of his publications compiled by Takács.
Dyakonov's family members are known for their contributions to various fields of knowledge, both sciences and humanities. His wife and two sons became well-known researchers and achieved ranks of full professors.
Igor's wife Nina Dyakonova (1915-2013), historian and critic of English literature with a special interest in English Romantic poetry of early 19 century (Keats, Byron, Shelley) and its reception in European and Russian literature. A student of Professors Viktor Zhirmunsky and Mikhail Alexeyev. Professor of her Alma mater Saint Petersburg State University and, later, teacher-training Herzen University.
Igor's sons became prominent physicists.