He studied piano with Rögnvaldur Sigurjónsson at the Reykjavík College of Music and took his diploma in 1957.
He went on to study at the State Academy in Cologne, Germany, from 1959, studying composition with Günter Raphael and Rudolf Petzold, instrumentation with Bernd Alois Zimmermann, conducting with Wolfgang von der Nahmer and piano with Hermann Pillney and Hans Otto Schmidt.
He took his diploma in composition and theory in 1963, a year in which he also attended summer courses in Darmstadt, making the acquaintance of Olivier Messiaen, Pierre Boulez, György Ligeti and Bruno Maderna.
In 1964 he studied with Karlheinz Stockhausen, Henri Pousseur, Christoph Caskel and Frederic Rzewski.
On 21 April 2019, Iceland's national public broadcasting service RÚV reported Atli Heimir's death.