He reports to Nick Theakstone, Group M’s UK chief executive, and replaces Mike Smallwood, who has left the business.
Greenhouse Group M was set up in 2015 after WPP won the Lloyds media account, then reported to be worth £100m.
Warren left MullenLowe last year, and has since been working as a strategic consultant to Studio of Art & Commerce.
Last week Group M announced it was looking for a new North America chief executive after Brian Lesser accepted a job with AT&T.
The WPP media agency network is in the middle of a wide-ranging restructure. Global chief executive Kelly Clark is overseeing a global merger of Group M agencies Maxus and MEC and trying to turn digital agency Essence into a fourth global media network.