He entered the Budapest Conservatory in 1924. He began a career as a solo violinist and in 1927 played a Richard Strauss composition under the composer’s baton. After having graduated from the Conservatory in 1930, he joined the Hungarian Trio with Ilonka Krauss and László Vencze.
In 1934 he became one of the founding members of the Hungarian String Quartet.
Végh left the Hungarian Quartet in 1940 to found his own quartet, the Végh String Quartet.
He and the quartet left Hungary in 1946. The quartet continued to give concerts until the mid-1970s.
He founded the International Chamber Music Festival of Cervo in 1962. He also founded the Sándor Végh Chamber Orchestra and conducted it from 1968 to 1971, and conducted the Marlboro Festival Orchestra (1974-77). In 1979 he became conductor of the Camerata Academica Salzburg at the Mozarteum.