Dodds, who was appointed joint managing director in November 2004, has been the sole managing director for the past year, following the departure of Guy Lambert, who left to take an equivalent position at Ogilvy Advertising in September 2006.
In his new role, Dodds will hold responsibility for the strategic management of OgilvyOne's on- and offline business, and will report to the chairman and chief executive of Ogilvy Group UK, Gary Leih.
Dodds will also oversee the management of the agency's subsidiary companies, which include the digital media planning and buying company Neo@Ogilvy, and the consulting operation Ogilvy Engage.
Having spent seven years at the agency, King will take over as the managing director, reporting to Dodds.
As a result of the restructure the client services director, Sam Williams-Thomas, has been promoted to the role of deputy managing director, which King has vacated.
Dodds said: "It's great to recognise talent and loyalty, something we in the Ogilvy family take seriously."
Leih said: "The momentum built up by Mike, Annette, Sam, and the rest of the team over the past year has been remarkable. They are meeting the challenge to drive our business to the front of digital developments in the UK."