Van Alexander was an acclaimed arranger, composer, and bandleader. He received a GRAMMY award for Ella Fitzgerald's first big hit A-Tisket, A-Tasket in 1938 and they recorded it together on his 23rd birthday. He went on to lead his own big band from 1939 to 1944 before moving to Los Angeles where he began a long career composing music for television shows and films. He also wrote First Arrangement, what Variety describes as “a landmark 1946 how-to book for musicians learning how to arrange for orchestra.”

Van worked with all the major singers of the day including Peggy Lee, Dinah Shore, Doris Day, Lena Horne, Bob Hope, and Tony Bennett. Alexander wrote band arrangements for Benny Goodman and Bing Crosby's brother Bob Crosby and penned music for The Mickey Rooney Show on TV. Alexander served as the head arranger for the Dean Martin Show from 1965 to 1974 and wrote scores for 1960s sitcoms including The Donna Reed Show, Bewitched, and I Dream of Jeannie. He was nominated three times in the 1970s for an Emmy for composition and music direction. In 1995, he received the first Irwin Kostal Tribute Award; in 1997, he was honored with a lifetime achievement award from the Los Angeles Jazz Society and received the same award from the ASCAP Foundation in 2002. Alexander was one of the original members of ASMAC and served on the Board, and as President, for many years.