De Leeuw was born on September 8, 1939, in Amsterdam. He studied piano and theory at the Amsterdam Conservatory and composition at The Hague Conservatory. As a student, he was interested in new and experimental music. He was one of the founders of the Dutch Charles Ives Society, and in 1969, he wrote a biography of Ives with poet J. Bernlef. In 1974, de Leeuw founded the Schoenberg Ensemble, based in The Hague, which specialized not only in the composers of the Second Viennese School but a broader repertoire ranging from the late 19th into the 21st centuries. The group performed and recorded so extensively with another new music ensemble, the ASKO Ensemble, that the two officially merged, and de Leeuw served as principal conductor. He was a guest conductor at the Aldeburgh Festival, the Royal Concertgebouw Orchestra, the New World Symphony, the RIAS-Kammerchor, the Netherlands Radio Chamber Orchestra, and the Netherlands Opera. From 1994-1998, he was the artistic director of the Tanglewood Festival of Contemporary Music, and he served as the artistic advisor for contemporary music for the Sydney Symphony Orchestra.
In his mature career, de Leeuw focused almost exclusively on works ranging from the early modern period through the contemporary. He was most closely associated with the music of Olivier Messiaen, György Ligeti, and Louis Andriessen. Each of the three composers employed musical languages of considerable complexity and sophistication that were notoriously difficult to perform, but their music was notable for an expressivity and directness of communication that was uncommon in an era when the majority of new music was considered "difficult" by audiences. De Leeuw's grounded understanding of distinctive idioms, and his commanding interpretations, made his performances of their music particularly riveting. As a pianist, he recorded works by Satie, Bartók, Stravinsky, Shostakovich, Ustvolskaya, Messiaen, and Górecki, as well as non-Europeans with a strong streak of individualism, including Ruth Crawford Seeger, George Antheil, Henry Brant, Steve Reich, Percy Grainger, and Claude Vivier.
De Leeuw was most active as a composer during the 1960s and '70s. He wrote several orchestral pieces, chamber music, and an opera, Reconstructie, based on the life of Che Guevara, written in collaboration with Andriessen, Misha Mengelberg, Peter Schat, and Jan van Vlijmen. In 2003, de Leeuw wrote Im wunderschönen Monat Mai, a radically free reimagining of 21 lieder by Schubert and Schumann, for singer and orchestra. In 2013, he wrote Der nächtliche Wanderer, a symphonic poem for orchestra. De Leeuw died in Amsterdam on February 14, 2020. ~ Stephen Eddins, Rovi