He was born in Helsinki, where he studied at the Sibelius Academy and was taught composition by Aarre Merikanto, Einojuhani Rautavaara, Einar Englund, and Joonas Kokkonen.
He continued his studies in Cologne with Bernd Alois Zimmermann; at the Juilliard School of Music in New York City with Vincent Persichetti and Eduard Steuermann; and privately in Poland with Witold Lutosławski.
[1] As professor of composition at the Sibelius Academy, Heininen has been highly influential in educating the next generation of Finnish composers and his pupils have included Magnus Lindberg, Kaija Saariaho, Jukka Tiensuu, Jouni Kaipainen and Veli-Matti Puumala.
In addition to composing original works, Heininen has reconstructed several pieces that his composition teacher Aarre Merikanto mutilated or destroyed, including the latter's Symphonic Study (1928) and String Sextet (1932) and written the violin concerto Tuuminki (A Notion) as a "re-imagining" of Merikanto's completely destroyed third violin concerto.
Alongside composition, Heininen has been active as a pianist, premiering and recording several of his own works.