Humber threw a perfect game for the Chicago White Sox against Seattle in 2012. But his ERA ballooned to 7.90 a year later with Houston and he hasn't pitched in the big leagues since.
Manager Andy Green said the 33-year-old Humber is "ready to move on with his family."
The Padres faced a Tuesday deadline to tell the lefty Thornton he made the roster or release him. He signed a minor league deal earlier this month.
Green also announced that right-hander Jon Edwards will start the season on the disabled list with elbow pain.