Levon Ambartsumian studied in the Moscow Gnessin Music School and then in the Moscow Tchaikovsky Conservatory. In 1977 he became the First Prize winner of Zagreb International Violin Competition headed by Henryk Szeryng. 

 Two years later he was a prizewinner of the Montreal International Competition, and in 1981 he won the All-Union Violin Competition in Riga.

Levon Ambartsumian was distinguished as Honored Artist of Armenia in 1988 and Honored Artist of Russia in 1997.

Since 1977 Ambartsumian has performed regularly in all the main cities of the Soviet Union and Eastern Europe as he was not permitted to accept invitations to travel to the West. Since 1988 he performed in the USA, Canada, Italy, France, Germany, Greece, Spain, Brazil, and South Korea.  In 1989 Ambartsumian founded the Moscow Chamber Orchestra ARCO which regularly performed in Russia and abroad and now resides in Athens, Georgia, USA.

Ambartsumian joined the faculty of the Moscow Tchaikovsky Conservatory in 1978 where he taught for 15 years.  For two years, he was a Visiting Professor at Indiana University School of Music (Bloomington, Indiana).  In 1995, Ambartsumian accepted the position of Franklin Professor of Violin at the University of Georgia School of Music (Athens, Georgia).

Ambartsumian devotes himself to contemporary Russian, Armenian and American Music and has made several important world premiers.  He has released 50 CD's including music by Wieniawski, Sarasate, Brahms, Mendelssohn, Tchaikovsky, Vivaldi, Stravinsky, Bartok, Shostakovich, Schnittke, Bronner, Arutiunian, and other contemporary composers.

In May 2009 Ambartsumian was awarded a gold medal of the Moscow Composers Union for to the development of contemporary music and music culture his contribution. As a teacher, Ambartsumian has given master classes in Russia, Armenia, South Korea, Canada, Portugal, Italy, France, Chile, and Brazil.  His former students hold principal positions in major European orchestras in Germany, France, Portugal, and Denmark, and many have been prizewinners at international Violin competitions.