Born in Tallinn, Kaljuste is the child of Heino Kaljuste (1925–1989), an Estonian choral conductor, and Lia Kaljuste, a radio journalist. Tõnu sang in his father's choirs as a child, and graduated from the Tallinn Music High School (Tallinna Muusikakeskkool) in 1971. He completed a graduate degree at the Tallinn Conservatory in 1976, studying with Jüri Variste and Roman Matsov, and continued as a postgraduate at the Leningrad Conservatory until 1978.
Kaljuste took his father's role as leader of the Ellerhein Chamber choir in 1974, an ensemble that performed choral works ranging from Renaissance music to contemporary avant-garde music. He was professor of choral conducting at the Tallinn Conservatory from 1978 to 1980, and won the Best Conductor prize at the 1980 Béla Bartók International Choral Competition. With financial support from the Estonian government, Kaljuste turned the Ellerhein Chamber Choir into a full-time ensemble, and renamed it the Estonian Philharmonic Chamber Choir in 1981. Kaljuste also conducted with the Estonian National Opera between 1978 and 1995.
After Estonia won independence in 1991, many of the barriers to international performing and recording were lifted, and Kaljuste became well known for his recordings on ECM Records of the works of Estonian composers such as Veljo Tormis, Erkki-Sven Tüür, Heino Eller, and Arvo Pärt. In 1993, he formed the Tallinn Chamber Orchestra; he was also principal conductor of the Swedish Radio Choir between 1994 and 2000, as well as of the Netherlands Chamber Choir (1998–2000).
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With Paul Giger
- Ignis (ECM, 1998)
- "Top 12 most outstanding Estonians in the world 2014". Estonian World. 1 February 2015. Retrieved 13 February 2015.