After his discharge from the Navy, he worked as a dance instructor at the Beverly Hills Hotel, where Latin band leader Bobby Ramos heard Costanzo playing bongos in a jam session and offered him a job.

Throughout the 1940s, Costanzo worked with several Latin bands, including a revived version of the Lecuona Cuban Boys, Desi Arnaz, and Rene Touzet.

He also played with the Billy May Orchestra, Peggy Lee, Danny Kaye, Perez Prado, Charlie Barnet, Pete Rugolo, Betty Grable, Harry James, Judy Garland, Patti Page, Jane Powell, Ray Anthony, Martin & Lewis, Frances Faye, Dinah Shore, Xavier Cugat, Frank Sinatra, Tony Curtis, and Eddie Fisher.

Many Hollywood stars studied bongos with him, including Marlon Brando, Rita Moreno, Carolyn Jones, Hugh O'Brian, Keenan Wynn, Van Johnson, Tony Curtis, Betty Grable, Vic Damone, James Dean, and Gary Cooper.

Costanzo died of complications from a ruptured abdominal aortic aneurysm at his home in Lakeside, California, on August 18, 2018, aged 98.