Schiff was born in Budapest into a Jewish family, the only child of two Holocaust survivors. He began piano lessons at age five, studying at the Franz Liszt Academy of Music in Budapest. He then studied in London with George Malcolm; Schiff made a recording with Malcolm of four-hand music by Mozart using a fortepiano that once belonged to the composer.
Schiff was a finalist in the Tchaikovsky International Piano Competition in 1974 and third prize winner of the Leeds International Pianoforte Competition in 1975. He emigrated from Hungary in 1979. He was unable to meet residency requirements for US citizenship due to his long absences for touring and accepted Austrian citizenship in 1987 and established homes in London and Salzburg.
From 1989 until 1998, Schiff was Artistic Director of the "Musiktage Mondsee" chamber music festival near Salzburg. In 1995, he co-founded the "Ittinger Pfingstkonzerte" in Kartause Ittingen, Switzerland, together with Heinz Holliger. From 2004 to 2007 he was Artist in Residence of the Kunstfest Weimar.
In 1999, he formed an occasional chamber orchestra, which he named the Cappella Andrea Barca. He has appeared as a conductor with several major orchestras, including regular appearances with Philharmonia Orchestra in London and the Chamber Orchestra of Europe, and recent ones with the San Francisco Symphony and Los Angeles Philharmonic.
Schiff is one of the most renowned interpreters of Bach, Mozart, Beethoven, Schubert and Schumann. In the 21st century, he has renounced the use of the sustain pedal when playing Bach.
Schiff is married to the violinist Yūko Shiokawa. The couple have residences in London and Florence, Italy.
He has been made an Honorary Professor by music academies in Budapest, Detmold and Munich and is a Special Supernumerary Fellow of Balliol College, Oxford University. He is a Fellow of the Royal Northern College of Music.
He was created a Knight Bachelor in the Queen's Birthday Honours list of 2014, for services to music.
Schiff has made public statements about politics in Austria and Hungary. He has also become an outspoken critic of the Hungarian government of Viktor Orbán, whom he has publicly accused of racism, anti-Semitism, and neo-fascism, stating in January 2012 that he would never again set foot in his native country. In 2000, he commented on the rise of the far right in Austria. He subsequently gave up his Austrian citizenship and took British citizenship in 2001.