The GMC, which monitors patient safety and standards of medical practice, is awaiting the findings of chief medical officer Sir Liam Donaldson's review following the Harold Shipman Inquiry.
The body has moved to streamline complaints procedures with doctors and wants to raise public confidence in the licensing and revalidation of doctors.
APCO emerged triumphant after a competitive pitch that involved six agencies before a final three-way contest against Luther Pendragon and Lexington Communications, Simpson's former employer. H&K declined to repitch.
APCO director Nick Sutcliffe will lead the account, supported by fellow director Darren Murphy, the former special adviser to the Prime Minister and ex-health secretary Alan Milburn.
The GMC uses different PA consultancies outside England. Grayling represents it in Scotland, Morgan Allen Moore in Wales and Chambre Public Affairs in N Ireland. H&K continues to advise it in Brussels.
Simpson joined in December from Lexington, where he was a senior consultant. Former GMC head of PA Matt Ball quit last year to be the top lobbyist at Accenture.