Lazarus will remain chairman of The Ogilvy Group, with both appointments effective from January 1 2009. She has been chief executive since 1996 and added the title of chairman in 1997.
Young has run Ogilvy in Asia Pacific for the past 13 years, and is credited with building the network into one of the market leaders in the world's fastest growing region.
The group is now the market leader in India and China, a prominent player in Japan, and successful in Korea, Vietnam, Indonesia and Thailand. The agency's Singapore hub is regarded as a creative hotbed.
In the past five years, the Ogilvy Asia Pacific region has almost doubled revenues to $500m.
Sir Martin Sorrell, chief executive of WPP, said: "Shelly has done a fantastic job as brand guardian of Ogilvy, building a first-class client roster and driving the company to fully embrace integrated marketing under 360 Degree Brand Stewardship and has taken Ogilvy from a strong position, both geographically and functionally, to a superb position.
"She'll be an extremely difficult act to follow and we are delighted she will continue to focus, as chairman of the Ogilvy Group, on developing Ogilvy's client relationships."
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Commenting on the appointment of Young, Sorrell said: "Miles brings to the role of CEO a deep understanding, not only of European and Asian markets, but also of the role that new technologies -- and integrated thinking - bring to our business.
"Shelly is certainly a 'gentlewoman' with brains. Miles is definitely a gentleman with brains. We are extremely lucky to have them both."
Prior to moving to Asia in 1995, Young had 12 years experience in Europe, where he began his marketing career in the early 1980s working at advertising agencies Lintas and Allen and Brady & Marsh, before joining Ogilvy & Mather in 1983.
In 1990, Young was appointed to lead Ogilvy's direct operations, the precursor to the agency's digital offering, in Europe, ultimately as chairman.
During this period he played a pivotal role in establishing the European hub for IBM when Ogilvy landed the global landmark account in 1994.