Atli Heimir Sveinsson was born in Reykjavík, Iceland 1938. At age of 10 he took piano lessons. At Reykjavík College of Music he studied piano with Rögnvaldur Sigurjónsson and took his diplom in 1957. He studied af Staatliche Hochschule für Musik in Cologna, Germany, from 1959.

He studied composition with Günter Raphael ang Rudolf Petzold, instrumentation with Bernd Alois Zimmermann, conductind with Wolfgang von der Nahmer and piano with Hermann Pillney and Hans Otto Schmidt. He also took private lessons with Gottfried Michael Koenig. Sveinson took his diploma in composition and theory in 1963. During this year he attented the summer courses in Darmstadt, making aquaintance to Oliver Messiaen, Pierre Boulez, Györgi Ligety, Bruno Maderna, a.o.

In 1964 he studied with Karlheinz Stockhausen at Kölner Kurse für neue Musik at Reiniscke Musikhochschule, among his teachers there wew Henry Pousseur, Christof Caskel, Frederick Rzewsky. In 1965 he went to Holland and studied electronic music with Gottfried Michael Koenig in Bilthoven.

Sveinsson has since lived in Iceland. He founded class of composition at Reykjavík Collega of music. Among his students are Atli Ingólfsson, Haukur Tómasson, Þorsteinn Hauksson, Kjartan Ólafsson and Helgi Pétursson. He was free lance producer at Icelandic State Broadcastind Service doing very popular programs on musical history.

Sveinsson was president of Icelandic Composers Assocation 1972-1983. He organised the festival and general assembly of International Socitety for Contemporary Music in Iceland in 1973. He was also president of the Nordic Composers Councel 1974ö1976 and organised the Nordic Music Days in Reykjavík 1976. In 1980 he founded Dark Music Days, a festival for contemporary Icelandic music.

In 1976 Sveinsson was awardes the Nordic Music Prize, given biannually by the five nordic countries Sweden, Norway, Iceland, Danemark and Finland, for his Flute Concerto Since 1992 Sveinsson receives a livetime honorary salary from the Icelandic Pariament. Sveinsson was elected menber of the Royal Swedish Academy of Music in 1993.