András Szőllősy was born in the Hungarian-Romanian-German multicultural city of Szászváros (Orăştie in Romanian, Broos in German) in Transylvania on 27 February 1921. In 1926 the family moved to Kolozsvár (Cluj, Romania), where Szöllösy attended the private music classes of Ilona Csipkés and completed his general studies at the Reformed College.

In 1939 he moved to Budapest and studied compo­sition at the Academy of Music with Zoltán Kodály and János Viski, and in 1947-48 with Goffredo Petrassi at the Accademia Santa Cecilia in Rome. Simultaneously with his musical studies, he also took a PhD. at the University of Budapest. As a student, he was a fellow of the Eötvös College (just like Zoltán Kodály four decades before him), a special school for selected students who later became eminent intellectuals.

Between 1939 and 1998 Szőllősy published over fifty important essays and studies. He published books on Kodály and Honegger, edited a collection of the writings of Bartók and Kodály, was the first to publish a comprehensive Bartók bibliography (1955) and compiled the list of Bartók's works (1956) every item in which has since been referred to with the legendary "Sz. number".

He found his own musical idiom relatively late; however, it is more accurate to say that his relentless self-criticism did not permit him to come out with fully authorized "serious" compositions before his Concerto No.3, completed in 1968 for sixteen strings. The latter won the title "Distinguished Composition of the Year" at UNESCO's Interna­tional Rostrum of Composers in 1970. In the years that followed he received many commissions, among others from The City of Budapest, the Ensemble M, The King's Singers, the BBC, the St Magnus Festival, the Orlando Festival and the Berliner Biennale.

Szőllősy's oeuvre, however, remained numerically rather small: it consists of some thirty titles only. In fact, he did not release  works that he considered not quite flawless. Nevertheless, besides what he considered "serious", he masterfully composed more than fifty film scores, incidental stage works and music for radio plays.

Szőllősy was Professor of Music History and Theory at the Liszt Academy of Music, Budapest, from 1950 until his retirement. In 1971 he was awarded the Erkel Prize and in 1985 the Kossuth Prize, the highest official recognition conferred by the Hun­garian State. In 1986 he received the Bartók-Pásztory Award. In 1987, the French government created him Commandeur de l'Ordre des Arts et des Lettres.

He died in Budapest on 7 December 2007.