Dessaix was born in Sydney and adopted at an early age. He was educated at North Sydney Boys High School. He studied in Moscow during the early 1970s, and taught Russian Studies at the Australian National University and the University of New South Wales from 1972 to 1984. During this time he translated a number of Russian books into English in collaboration with Michael Ulman, including The Sheepskin Coat and An Absolutely Happy Village by Boris Vakhtin.
From 1985 to 1995 he presented the ABC program Books and Writing.
His first book was his autobiography, A Mother's Disgrace which was published in 1994 by HarperCollins. ISBN 0-207-17934-4 Manuscripts concerning A Mother's Disgrace are in the Mitchell Library of New South Wales. The manuscript was written in French, and the book concerns his journey to an alternative sexuality after twelve years of marriage and his meeting with his birth mother Yvonne. It was made into a screenplay by Ross Wilson in 1999.
His first fictional work, Night Letters, was published in 1996 and worked on as early as 1994. It was translated into German, French, Italian, Dutch, Finnish and Portuguese. ISBN 0-312-19939-2
His second novel was Corfu which was published in 2001. ISBN 0-330-36278-X
Dessaix' latest long work, Twilight of Love: Travels with Turgenev defies genre characterisation, interweaving a personal travelogue with a biography of Turgenev. It was published in 2004. It takes inspiration from his doctoral thesis on Turgenev and the Soviet Union, as well as Alain de Botton's works on travel, art and philosophy. ISBN 1-59376-063-9