Muir, 37, rose up the ranks at Ogilvy & Mather before replacing Mandy Pooler as chief executive of The Channel in the beginning of 2005.
An announcement from 10 Downing Street is expected this morning. Muir was unavailable for comment.
LONDON - David Muir, WPP stalwart and chief executive of its Channel division, is quitting the holding company for a job at 10 Downing Street.
Join a growing community of media, marketing and advertising professionals today
Read exclusive registrant only articles
Read more articles each month
Sign up for free specialised news bulletinsRegister Now
Get the very latest news and insight from Campaign with unrestricted access to campaignlive.co.uk ,plus get exclusive discounts to Campaign eventsBecome a member