Tiensuu was born in Helsinki. After extensive musical studies (piano, harpsichord, conducting, composing, historically informed performance, electroacoustic and computer music a.o.t.) at the Sibelius Academy, Helsinki (1967–1972), the Juilliard School, New York (1972–1973), Hochschule für Musik Freiburg (1974–1976), IRCAM, Paris (1978–1982) and other institutes Jukka Tiensuu toured three continents giving numerous concerts with a wide repertoire ranging from the Renaissance to the latest avant-garde and performing both classical and free improvisations. He has received numerous prizes for his compositional work as well as for his recordings and performances. In 2020, he won the Wihuri Sibelius Prize. According to the jury report his "compositions emanate a deep spirituality, and his unwavering adherence to artistic goals is impressive".
Along with over a hundred works in the traditional instrumental, vocal and orchestral fields – in various styles, often microtonal and with electronic or computer music parts – Tiensuu's compositional output also includes many curiosities such as works for Chinese orchestra, accordion ensemble, clarinet choir, instrumental theatre, Baroque orchestra, jazz orchestra, kantele, sheng and works for any ensemble. Most of his works have remained in the repertoire and are available on disc.
His compositions have been premiered by major orchestras and ensembles in three continents by conductors such as Susanna Mälkki, Ernest Bour, Sakari Oramo, Jukka-Pekka Saraste, Lorraine Vaillancourt, Diego Masson, Ilan Volkov, Leif Segerstam, Jacek Kaspszyk, John Storgårds, Hannu Lintu, Dima Slobodeniuk, Yan Huichang, Juha Kangas, Jacques Mercier, Stefan Asbury, among others.
In the late 70's, as the president of the ISCM Finnish Section, Tiensuu started the first ever regular contemporary music concert series in Helsinki. He then became a founder and the first artistic director of Helsinki Biennale (now Musica nova Helsinki) as well as the founder and a long-time artistic director of Time of Music contemporary music festival and summer academy in Viitasaari. His other activities include teaching, writing for books and magazines and making evocative radio programs on both baroque music and on music of our time. According to Finnish Music Quarterly (3/2007) Jukka Tiensuu's influence on the contemporary Finnish music scene is virtually beyond compare.