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.[2]

After Spooky Tooth split up in 1974, Wright continued his solo career, culminating in "Dream Weaver". The single peaked at #2 for three weeks on the Billboard Hot 100 in 1976, sold over one million copies, and was awarded a gold disc by the RIAA in March 1976.[3] It was later featured in the Wayne's World feature film and soundtrack album as well as in the 1996 film The People vs. Larry Flynt and 2010's Toy Story 3. Later in 1976, his follow-up single "Love Is Alive" also reached #2 (for two weeks).

Ronnie Montrose played guitar on the song "Power of Love" from Wright's album, The Dream Weaver.

Although The Dream Weaver was a hit album and would go multi-platinum, his subsequent releases were not nearly as popular, either critically or commercially, and his career quickly stalled. But Wright continued to make albums throughout the 1970s, 1980s, and 1990s. Wounded Bird Records reissued The Light of Smiles, Touch and Gone, Headin' Home and The Right Place in October 2008; all except Headin' Home featured extra tracks.

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).

His 1981 song "Comin' Apart", from the album The Right Place, was sampled by Armand Van Helden for the 2004 club song titled "My My My". The song was remixed in 2006 by Andreas S. Jensen. "Heartbeat", also from The Right Place, was re-recorded in 2007 as a dance track by Topmodelz. In 1984 Chaka Khan included her cover version of "Love Is Alive" (re-titled "My Love Is Alive") on her album I Feel for You.

In 1986, Wright contributed the song "Hold On to Your Vision" to the soundtrack of the Sylvester Stallone movie Cobra.

"Better By You, Better Than Me," a song written by Wright for Spooky Tooth, was covered by Judas Priest on their 1978 album Stained Class.

In 2008, Wright toured with Ringo Starr & His All-Starr Band. In November 2008, Wright released the six-track EP, Waiting to Catch the Light, on the Larkio Music label. In late 2008, Wright also released The Light of a Million Suns, which featured a re-recorded version of "Love Is Alive" in which son Dorian gets a recording credit.

In 2010, Wright toured again with Ringo Starr & His All-Starr Band, along with Rick Derringer, Edgar Winter, Richard Page, Wally Palmer, and Gregg Bissonette.

Wright released a new album in June 2010 called Connected. Special guests on the record include Ringo Starr, Joe Walsh, and Jeff "Skunk" Baxter.