The 74-year-old Scot, who was world champion three times, has switched from IMG to Just Marketing International.
"I've been with IMG since 1968," he said. "Mark (McCormack) signed me up and they've done very well for me over the years but they are not in Formula One and haven't been in Formula One now for a good long time."
American lawyer McCormack, who died in 2003, founded the International Management Group (IMG) in 1960. Golfer Arnold Palmer was his first client.
Unlisted JMI, founded by American former professional driver Zak Brown, was acquired by British sports marketing group Chime Communications PLC in October for $71 million (£43m).
They arrange sponsorship, hospitality and rights deals in F1, NASCAR and IndyCar.