Gomori was born in Budapest in 1934. From 1953 to 1956 he studied Hungarian and Polish at Eötvös Loránd University. He took part in the 1956 revolution both as a student organiser and editor of the newspaper Egyetemi ifjúság (University Youth). After the suppression of the revolution he fled to England and continued his studies at the University of Oxford where in 1962 completed a B.Litt. thesis on Polish and Hungarian literature later published as his first book in English (Polish and Hungarian Poetry 1945 to 1956; Oxford,1966). Between 1958 and 1961 he was member of the Executive of the Hungarian Writers Association Abroad.
His first teaching job was at the University of California, Berkeley, after which he researched at Harvard University (1964–65). Having spent four years as researcher and librarian at the University of Birmingham, in 1969 he took up a position at the University of Cambridge teaching Polish and Hungarian literature until his retirement in 2001.
In May 2017 he was appointed as Senior Research Associate of the UCL School of Slavonic and East European Studies.
He has published twelve books of poetry in Hungarian, four in English and one in Polish, and is the author of numerous critical works on Polish and Hungarian literature, the latest of which were Magnetic Poles (London, 2000), and Erdélyi Merítések ("Transylvanian Catches", Cluj-Kolozsvár, 2004). With Clive Wilmer he has translated two books of poems by Miklós Radnóti (1979, 2003), two collections by György Petri (1991,1999, the second collection shortlisted for the Weidenfeld Translation Prize) and co-edited with George Szirtes a representative anthology of modern Hungarian poetry, The Colonnade of Teeth (Bloodaxe Books, Newcastle, 1996). From 1992 to 2006 he was a member of the Executive of the Association of the Hungarian Language and Culture of Budapest, also serving on the Board of the Hungarian Writers' Association (2001–2004).
In 1995 he was awarded the Officer's Cross of the Republic of Hungary and in 2007 the Commander's Cross of the Republic of Hungary. His literary and scholarly prizes include the Jurzykowski Award (1972), Medal of the Polish Committee of National Education (1992), Salvatore Quasimodo Prize (1993), the Ada Negri Memorial Prize (1995), the Pro Cultura Hungarica (1999) the Lotz Memorial Medal (2006), and the Alföld Prize (2009). He is a member of the Hungarian PEN Club and the Society of Hungarian Studies (London), also of the Polish Academy of Arts and Sciences (PAU) of Cracow. In 2014 he was awarded the Janus Pannonius prize for Translation of Poetry and the Hídverő ('Bridge Builders') Prize in Székelyudvarhely, Romania.
In 2014 he was made Senator of the University of Szeged in recognition of his scholarly and artistic achievements.
Gömöri is a regular contributor to the British press (The Guardian, The Independent) as well as to the American bimonthly World Literature Today. Several essays of his were published in Polish publication Odra Wrocław. He also continues publishing in Hungarian, English and Polish. His reminiscences of Czesław Miłosz were included in Cynthia L. Haven's An Invisible Rope: Portraits of Czesław Miłosz in 2011.
He is also a member of Trinity College, Cambridge and emeritus fellow of Darwin College, Cambridge, where for a number of years edited the college newsletter. For over three decades he has been on the Editorial Board of the American quarterly Books Abroad and its continuation World Literature Today. He is also on the editorial board of Lymbus Budapest and Litteraria Copernicana Toruń.
2014 saw a new book of his poetry published, Rózsalovaglás (Riding with Roses), by Pro Pannonia Publishers and his collected essays on the late Renaissance poet Bálint Balassi (A rejtőzködő Balassi) published in Hungarian by Komp-Press in Romania. His latest poetry collection in English, Polishing October: New and Selected Poems (Shoestring Press) was recently reviewed in World Literature Today.
He has two daughters from his first marriage and some years ago he moved to London to be near to his two sons, Pete and Ben, and his stepson, Daniel.