Khayyam was born as Sa'aadat Hussain in undivided Punjab in Rahon, a town in Nawanshahr District which was then the Nawanshahr tehsil of Jalandhar District. As a boy Khayyam ran away to Delhi to learn music but was forced to return to complete his education. Khayyam then went to Lahore to learn music from the famous Baba Chishti.

He was never interested in studies and was always fascinated by the music of Indian cinema. He was inclined to music since a very young age. He often escaped to the city to watch movies. Khayyam soon ran away to his uncle's house in Delhi, in the hope of becoming an actor. Khayyam's uncle enrolled him in a school, but when he saw his passion for films, he allowed him to learn music, which was actually a step forward in realizing his ambitions. He got his training in music under Pandit Amar Nath.