Earlier, reports suggested that the ex-footballer had refused to appear on yesterday's programme due to unhappiness with the show's new format.
According to the Daily Mail, Wright was unhappy with having to promote the channel's talent show Don't Stop Believing.
"Ian wouldn’t have walked out because it would have been unprofessional. He had even been coming in in a wheelchair and then crutches after the operation," a source claimed.
"But to be honest he doesn't need to do it, so it's probably best to be off what is now a steadily sinking ship."
Confirming his departure, a spokesperson stated: "Ian will no longer be appearing on Live From Studio Five."