Tamás Vásáry made his stage debut at the age of 8, performing Mozart's Piano Concerto in D major, K.107 in the city of his birth, where he gave a solo recital the following year. He then began to concertize regularly as a child prodigy. It was at this time that he was introduced to Ernő Dohnányi, the leading figure of musical life in Hungary, who made a unique exception by offering to accept the gifted youth as a pupil in spite of his age. Vásáry studied only a short time under his tutelage, however, as Dohnányi soon left Hungary.

He also studied with József Gát and Lajos Hernádi at the Franz Liszt Academy of Music in Budapest, and was later assistant there to Zoltán Kodály, who made him a gift of a Steinway piano to help the emerging talent.

At the age of 14 Vásáry won first prize in the Franz Liszt competition at the Academy of Music in Budapest, in 1947. He left Hungary in 1956 and settled in Switzerland. He made his débuts in the major cities of the West in 1960 and 1961. He has subsequently resided in London, England. He has made many recordings for Deutsche Grammophon, particularly of the Romantic repertoire, especially Frédéric Chopin, Franz Liszt and Sergei Rachmaninoff.

As a conductor, Vásáry served as joint artistic director of the Northern Sinfonia from 1979 to 1982, sharing the post with Iván Fischer. With the Northern Sinfonia Vásáry recorded the Chopin piano concertos, directing from the keyboard. Vásáry was later Principal Conductor of the Bournemouth Sinfonietta, from 1989 to 1997. Between 1993 and 2004 he was the Principal Conductor of the Hungarian Radio Orchestra. He has guest conducted many of the principal British orchestras as well as appearing regularly in the United States and elsewhere as pianist and conductor.

He was awarded the UNESCO Mozart Medal in 2012 in recognition of his talent and dedication to the universal values that inspire UNESCO.