Rigby, currently Lowe's head of account management, will succeed Sven Olsen, who becomes the director of client services for FCB Europe.
Rigby will form the basis of a new management team to replace the managing partners, Paul Houlding and Steve Hastings, and the joint creative directors, Rob Fletcher and Dave Alexander, who resigned in March and plan to launch a start-up later this year.
The result will be an entirely new management line-up at the UK's 19th-ranked shop. It plans to have a new creative director and planning chief in place by September.
Rigby's appointment is part of plans by John Banks, the agency's chairman and chief executive, to improve what he described as its "lousy" new-business record and to meet the demanding targets set by its Interpublic parent.
Banks said he wanted to restructure the agency, which is expected to readopt its old Foote Cone & Belding name, to make it a more potent rival to more recent arrivals such as Mother and Clemmow Hornby Inge.
"We have to learn from the way these agencies are winning the large accounts," he added. "That means being braver, more entrepreneurial and more leading edge."
The agency aims to make itself more flexible and valuable to existing and potential clients by bringing media planning and PR into the heart of its activities and generating integrated creative solutions.
Rigby, 34, a former Lowe new-business director, said: "John is starting afresh with a blank sheet of paper and there's a complete meeting of minds between us."
However, Lowe this week indicated that it may not be able to release Rigby immediately because of his role on key pieces of Unilever business.
Tim Lindsay, the president of Lowe & Partners Worldwide, said: "It's always flattering when an agency draws from the ranks of our middle managers for its managing director."