Doráti was born in Budapest, his father a violinist with the Budapest Philharmonic Orchestra. Doráti studied music there, his teachers including Zoltán Kodály and Leo Weiner for composition and Béla Bartók for piano, at the Franz Liszt Academy. He made his conducting debut in 1924 with the Budapest Royal Opera. He made his first recording with the London Philharmonic for the recording label His Master's Voice, which later became RCA. Over the course of his carreer Doráti made over 600 recordings.
Doráti held posts as principal conductor of the Dallas Symphony Orchestra (1945-48), practically creating that orchestra from scratch; the Minneapolis Symphony Orchestra (1949-60), the BBC Symphony Orchestra (1963-66), which bid him a fond farewell playing his Symphony in Five Movements and his Madrigal Suite; the Stockholm Philharmonic (1966-70), with which he recorded his Symphony No. 1 and his Symphony No. 2, "Querela Pacis" on the BIS label, and taking that orchestra on its first tours ever; the National Symphony in Washington, D.C. (1970-77), which he rescued from bankruptcy and a players' strike; the Detroit Symphony Orchestra (1977-81), restoring them to 'world-class status' in their newly renovated Orchestra Hall; and the Royal Philharmonic Orchestra (1975-79). He conducted the world premiere of Tibor Serly's completion of Bartók's Viola Concerto with the Minneapolis Symphony in 1949. He made many recordings, notably of pieces by Bartók and Kodály and the complete symphonies of Joseph Haydn with the Philharmonia Hungarica.
As well as composing wholly original pieces, he arranged pieces by Johann Strauss II for the ballet Graduation Ball, as well as Offenbach's La Belle Hélčne and Bluebeard, and Mussorgsky's Fair at Sorotchinsk.
Queen Elizabeth II awared Doráti Knight of the British Empire. His autobiography, Notes of Seven Decades, was published in 1979.