Becker was born in Henderson, Kentucky, and began his formal musical education at the Cincinnati Conservatory, receiving his diploma in 1905. He then pursued graduate studies at the Wisconsin Conservatory of Music, where he earned a doctorate in composition in 1923. After a period of comparative obscurity, his career as an educator and administrator began in 1917 at the University of Notre Dame, where he taught for ten years. A devout Catholic, he relocated to another Catholic institution, the College of St. Thomas, in St. Paul, Minnesota, where he taught from 1929 until 1933. In the early 1930s he was especially active as a conductor, giving midwestern premieres of works by his close friend Charles Ives, as well as music by Carl Ruggles and Wallingford Riegger. From 1935 to 1941 he administered the Federal Music Project in Minnesota, and for a time was associate editor of the New Music Quarterly, founded by Henry Cowell, whom he had first met in 1928. He returned to teaching at Barat College in Lake Forest, Illinois from 1943 until his retirement in 1957.