Hovhaness's parents soon supported their son's precocious composing, and set up his first piano lessons with a neighborhood Teacher. Hovhaness continued his piano studies with Adelaide Proctor and then Heinrich Gebhard. By age 14 he decided to devote himself to composition. Among his early musical experiences were Baptist hymns and recordings of Gomidas Vartabed, an eminent Armenian Composer. He composed two operas during his teenage years which were performed at Arlington High School, and Composer Roger Sessions took an interest in his music during this time. Following his graduation from high school in 1929, he studied with Leo Rich Lewis at Tufts and then under Frederick Converse at the New England Conservatory of Music. In 1932, he won the Conservatory's Samuel Endicott prize for composition with his Sunset Symphony (elsewhere entitled Sunset Saga).

During the 1930s and 1940s, Hovhaness famously destroyed many of his early works. He later claimed that he had burned at least 1000 different pieces, a process that took at least two weeks; elsewhere he claimed to have destroyed around 500 scores totaling as many as a thousand pages. In an interview with Richard Howard, he stated that the decision was based primarily on Sessions' criticism of his works of that period, and that he wanted to make a new start in composition.

In July 1934, Hovhaness traveled with his first wife, Martha Mott Davis, to Finland to meet Jean Sibelius, whose music he had greatly admired since childhood. The two continued to correspond for the next twenty years. In 1935, Hovhaness named his daughter and only child from his first marriage Jean Christina Hovhaness after Jean Christian Sibelius, her godfather and Hovhaness's friend for three decades.

In 1936, Hovhaness attended a performance in Boston by the Indian dance troupe of Uday Shankar (with orchestra led by Vishnudas Shirali), which inspired his lifelong interest in the music of India. During the 1930s (until 1939), he worked in Franklin D. Roosevelt's Federal Music Project.

In the mid-1940s, Hovhaness' stature in New York was helped considerably by members of the immigrant Armenian community who sponsored several high-profile concerts of his music. This organization, the Friends of Armenian Music Committee, was led by Hovhaness's friends Dr. Elizabeth A. Gregory, the Armenian American piano/violin duo Maro Ajemian and Anahid Ajemian, and later Anahid's husband, pioneering record Producer and subsequent Columbia Records executive George Avakian. Their help led directly to many recordings of Hovhaness' music appearing in the 1950s on MGM and Mercury records, placing him firmly on the American musical landscape.

Lou Harrison reviewed a 1945 concert of Hovhaness' music which included his 1944 concerto for piano and strings, entitled Lousadzak:

In May and June 1946, while staying with an Armenian family, Hovhaness composed Etchmiadzin, an opera on an Armenian theme, which was commissioned by a local Armenian church.

In 1948 he joined the faculty of the Boston Conservatory, teaching there until 1951. His students there included the jazz Musicians Sam Rivers and Gigi Gryce.

Hovhaness was inducted into the National Institute of Arts and Letters (1951), and received honorary D.Mus. degrees from the University of Rochester (1958), Bates College (1959) and the Boston Conservatory (1987). He moved to Seattle in the early 1970s, where he lived for the rest of his life. In 1973, he composed his third and final ballet score for Martha Graham: Myth of a Voyage, and over the next twenty years (between 1973 and 1992) he produced no fewer than 37 new symphonies.

His biggest breakthrough till then came in 1955, when his Symphony No. 2, Mysterious Mountain, was premiered by Leopold Stokowski in his debut with the Houston Symphony, although the idea that Mysterious Mountain was commissioned for that orchestra is a Common misconception. That same year, MGM Records released recordings of a number of his works. Between 1956 and 1958, at the urging of Howard Hanson, an admirer of his music, he taught summer sessions at the Eastman School of Music long presided over by Hanson.

In the mid-1960s he spent several summers touring Europe, living and working much of the time in Switzerland.

He then studied Japanese gagaku music (learning the wind instruments hichiriki, shō, and ryūteki) in the spring of 1962 with Masatoshi Shamoto in Hawaii, and a Rockefeller Foundation grant allowed him further gagaku studies with Masataro Togi in Japan (1962–63). Also while in Japan, he studied and played the nagauta (kabuki) shamisen and the jōruri (bunraku) shamisen. In recognition of the musical styles he studied in Japan, he wrote Fantasy on Japanese Woodprints, Op. 211 (1965), a concerto for xylophone and orchestra.

He and his then wife then set up a record label devoted to the release of his own works, Poseidon Society. Its first release was in 1963, with around 15 discs following over the next decade. Following their divorce, the rights to this catalog were acquired by Crystal Records.

In 1965, as part of a U.S. government-sponsored delegation, he visited Russia as well as Soviet-controlled Georgia and Armenia, the only time he visited his paternal ancestral homeland. While there, he donated his handwritten manuscripts of harmonized Armenian liturgical music to the Yeghishe Charents State Museum of Arts and Literature in Yerevan.

Hovhaness stated in a 1971 interview in Ararat magazine:

Continuing his interest in composing for Asian instruments, in 1981, at the request of Lou Harrison, he composed two works for Indonesian gamelan orchestra which were premiered by the gamelan at Lewis & Clark College, under the direction of Vincent McDermott.

Significant archives of Hovhaness materials, comprising scores, sound recordings, photographs and correspondence are located at several academic centers, including Harvard University, University of Washington, the Library of Congress in Washington, D.C., the Armenian Cultural Foundation in Arlington, MA, and Yerevan’s State Museum of Arts and Literature in Armenia.