He was born in Port-au-Prince, Haiti, of a Puerto-Rican mother and an American father. While living in Costa Rica, at age ten, he studied the violin with Hugo Mariani, who was at the time the conductor of the National Symphony Orchestra of Costa Rica. Holdridge decided he wanted to become a composer at age fifteen, and then moved to Boston, where he finished high school and studied composition with Henry Lasker.
As an adult, Holdridge moved to New York City to continue his music studies and begin his career as a professional composer. There, he composed chamber works, rock pieces, songs, theater music and background scores for short films, and eventually came to Neil Diamond's notice. Diamond then brought Holdridge with him to Los Angeles to write arrangements for his forthcoming albums. After several gold and platinum hits, the two collaborated on the film score for Jonathan Livingston Seagull.
Holdridge has composed, conducted, and orchestrated for many films, some of the most notable being Puerto Vallarta Squeeze, Unlikely Heroes, Beautiful Music, Ever Again, Into The Arms of Strangers: Stories of The Kindertransport and Brothers at War. He has also composed for several television series, including The Mists of Avalon, American Family, and The Brooke Ellison Story.
Holdridge has performed and recorded in several concerts, including The Golden Land, the Jefferson Tribute, his suite from the opera Lazarus And His Beloved, the Concerto For Viola And Chamber Orchestra, the Concertino For Violoncello And Strings, the Serenade For Oboe And Strings, the Fantasy Sonata For ?Cello and Piano, the Elegy For Strings and Harp, and Sonnet for soprano and orchestra. He has also written, arranged and conducted for recording artists such as Placido Domingo, Barbra Streisand, Brian May of Queen, Stevie Wonder, John Denver, Neil Sedaka, Daniel Rodriguez, Al Jarreau, George Benson, Peabo Bryson, Dionne Warwick, Diana Ross, Natalie Cole, and Jane Olivor.