Fudge was the president of Kraft's $5 billion beverages and desserts division until 2001, responsible for core brands such as Maxwell House.
She will oversee the entire WPP-owned network, including Burson-Marsteller and Wunderman, and becomes the first black leader of a major ad network.
Dolan leaves amid speculation that he and the WPP chief executive, Sir Martin Sorrell, had clashed over the future of Y&R. It is unclear what his future plans are.
As well as holding an MBA from Harvard, Fudge sits on the boards of General Electric, Honeywell International and Marriot International.
"I look forward to working with the talented people of Y&R to continue to deliver outstanding work for our client partners and build upon the great legacy of this company," she said.