The start-up opens its doors this week, with the food packaging giant Tetra Pak and the global telecoms operator Telenor as its founding clients.
Green Cave People will be based in London's Great Titchfield Street, and will focus on "creating powerful, entertaining advertising that gets noticed, remembered and acted upon".
The agency is expected to add to its management team within the next few weeks.
Green began his career at Saatchi & Saatchi, before spells at DDB UK, CDP, WCRS and McCann Erickson. In 2000, he became one of the founding partners of DLKW.
Green left the agency in April 2008 following its acquisition by Creston, and later that year joined Naked Communications. He moved to Beta a year later, where he worked on campaigns for Jackpotjoy and NSPCC.
Cave spent the majority of his career within the Lowe network, holding positions including the managing partner of Lowe Howard-Spink, strategy director of Lowe Group and president of Lowe Digital. He launched the integrated agency Drugstore in 2001, which was acquired by Erasmus in September 2008.