Born in Seattle, Washington, Alexander began performing in his teens as a singer and dancer in vaudeville productions.
In 1939, he moved to New York City, where he arranged and composed music for radio programs, including Benny Goodman's Camel Caravan (as "Myer Alexander"), "The Lucky Strike Show" and "Amos 'n' Andy".
[6] He directed the chorus for The Star Theater,[7] Great Moments in Music[8] and (billed as Myer Alexander) the Goodman program.
[11] Although credited to Axel Stordahl, it was Alexander who arranged "The House I Live In" for Frank Sinatra, recorded in 1945.
[citation needed] In 1944, Alexander and Lyn Murray, along with business manager Eugene Loewenthal, formed Murray-Alexander Associates in New York City.