Riegger was born in 1885 to Ida Wallingford and Constantine Riegger. After his father's lumber mill burned down in 1888, his family moved to Indianapolis, and later to Louisville, finally settling in New York in 1900. A gifted cellist, he graduated from the first graduating class of the Institute of Musical Art, later known as the Juilliard School, in 1907, after studying under Percy Goetschius. He continued his studies at the Hochschule für Musik in Berlin for three years. After returning in 1910, he married Rose Schramm, with whom he later had three daughters, in 1911. For a time, he returned to Germany and accepted various conducting positions, but this was interrupted by the joining of America in World War I in 1917, after which he moved back to America. From 1918 to 1922, he taught music theory and violoncello at Drake University. During the greater part of the time from 1930 to 1956, he continued publishing music and taught at various universities in New York, notably the Institute of Musical Art and Ithaca College. In 1957, he was called before the House Un-American Activities Committee, which was investigating Communism in the musical world. In 1958, Leonard Bernstein honored him by conducting his Music for Orchestra with the New York Philharmonic Orchestra. He died in New York in 1961 when he tripped over the leashes of two fighting dogs, resulting in a fall and a head injury from which he did not recover despite treatment.
His students included Alan Stout.
Early on in his career as a composer, the style of his compositions was markedly different from that of his later work, which mostly used the twelve-tone system. His compositions, following those of Goetschius, were somewhat romanticist.
Starting in the mid 1930's, Riegger began to write contemporary dance music. Later, as his career progressed, he began to use Schoenberg's twelve-tone technique more and more often, though he did occasionally revert to his earlier styles. From 1941 on, he focused almost solely on instrumental music, and his Symphony No. 3 received the New York Music Critics' Circle Award and a Naumburg Foundation Recording Award.