Bolet was born in Havana in Cuba and studied at the Curtis Institute of Music in Philadelphia, where he himself taught from 1939 to 1942. His teachers included Leopold Godowsky, David Saperton, Moriz Rosenthal and Fritz Reiner.

In 1942 Bolet joined the US Army and was sent to Japan. While there, he conducted the Japanese premiere of The Mikado. He made his first recordings for Remington. He provided the piano soundtrack for the 1960 film about Liszt, "Song without End". His playing, though, was condemned by American critics for decades as too focused on virtuosity. Hence he only made a few recordings for smaller labels in the 1960s. He only came to prominence with a stupendous recital at Carnegie Hall 1974 which set a seal on his reputation.

Bolet showed exactly what he could do and his phenomenal playing can be heard on CDs issued most recently by PHILIPS in their Great Pianists Series. He later became Head of Piano at the Curtis Institute, succeeding Rudolf Serkin, but retired from this to concentrate once again on his career. In 1984, the A&E Network broadcast a series of three programs entitled Bolet Meets Rachmaninoff, in which the pianist was shown giving masterclasses on Piano Concerto No. 3 (Rachmaninoff), or, as it is popularly known, "The Rach Third". This is followed on the series by a complete performance of Bolet playing the concerto.

The DECCA/London recording company contracted him in 1978, so that Bolet got his first major record contract at the age of 63. They made recordings of key sections of his repertoire from 1978 up to his death, but there are also tapes of many live concerts which can be found in archives, principally the International Piano Archive at Maryland. These include a speciality of his, which he studied with the composer himself: J. Strauss/L.Godowsky Fledermaus paraphrase.

Bolet is particularly well remembered for his performances and recordings of large-scale Romantic music, particularly works by Franz Liszt and Frederic Chopin. He also specialised in piano transcriptions and unusual repertoire, including the fiendishly difficult works of Godowsky, many of which Bolet had studied with the composer himself. In an interview given to Elyse Mach, Jorge Bolet extensively mentioned the "Romantic Piano Concerto" by Joseph Marx which was, according to Bolet's own words, his favorite among the great virtuoso concertos because of the enormous show of strength required from the soloist.

Bolet died in 1990 in Mountain View, California from AIDS-related diseases.