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".