Fudge will remain chairman and CEO of Y&R Brands, which houses PR agency Burson-Marsteller, branding agency Landor Associates and direct marketing agency Wunderman.
McLennan worked for 17 years at George Patterson Y&R, formerly George Patterson Bates, which was acquired last year by WPP.
He said: "It's a great privilege to be part of the Y&R global team and I look forward to working with our people and our clients to lead our business into the future."
Fudge said: "Hamish has been a rising star at the agency. He has an outstanding track record in the business and I am delighted to have him as my partner at Y&R."
It was reported back in April that Fudge, a former president of Kraft Foods, was set to move aside.
In an interview with Business Week, Fudge said that she and WPP were looking for someone to replace her as head of the agency, but she would remain in charge of Y&R Brands.
Fudge's position looked increasingly untenable since Y&R's early elimination from the $100m review for Ford-owned marque Jaguar. The loss compounded the effects of previous client defections, in which Sony Electronics, Computer Associates, Kraft Foods and Burger King have all left the agency.
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