In 1959, Wright made his first commercial recording with Billy Markle as the duo Gary & Billy for the 20th Century Fox Records record label. The songs released were "Working After School" and "Lisa". In the 1960s, Wright went to Europe to continue studying psychology. In 1967, he joined the band Spooky Tooth as singer and keyboardist. In 1970 Wright was involved as a record producer with the Liverpool based folk music band Arrival, and he was also a member of the folk rock band Howl the Good who had played alongside Arrival at the Isle of Wight Festival 1970. During this period, he also befriended George Harrison and was invited to contribute piano to Harrison's All Things Must Pass. round this time he also played piano on Nilsson's "Without You". On November 23, 1971, Wright appeared on an episode of The Dick Cavett Show in a band called Wonder Wheel, performing "Two Faced Man", a song he wrote. George Harrison plays slide guitar in this band as a favor, since Wright had played piano on Harrison's album All Things Must Pass.

After Spooky Tooth split in 1974, Wright continued his solo career, culminating in his album The Dream Weaver and its title track "Dream Weaver". The single peaked at #2 for three weeks on the Billboard Hot 100 in 1976, sold over one million copies. The song was awarded a gold disc by the RIAA in March 1976.Wright's last success on the Billboard Hot 100 was in 1981, when he returned with "Really Wanna Know You" (co-written by Ali Thomson)