In a surprise move, Carter joined the Prime Minister's team after being approached at the end of last year. Brown and Brunswick founder Alan Parker already have close ties - Brown is a godfather to Parker's son William.
Media commentators are already questioning whether Brunswick's blue-chip client list - including British Airways, Barclays and Diageo - will present Carter with conflicts of interest.
No shortlist has yet been drawn up for the position at Brunswick, which is thought to be one of the best-paid in UK agency PR.
Brunswick senior partner Susan Gilchrist said that Paris-based senior partner Laurent Perpere would head the agency's management executive committee until a successor to Carter is found.
Former Ofcom chief executive Carter joined Brunswick in March, having previously been tipped for the top job at ITV (PRWeek, 8 December 2006).
- Brunswick launched its San Francisco office this week, with clients including Gap and Visa.