No immediate successor has been named, which suggests that Sir Martin Sorrell, the chief executive of Y&R's WPP parent, will bide his time before taking any action.
His unwillingness to move quickly is thought to be linked with what is seen as Fudge's underwhelming term as the chairman and chief executive of Y&R Brands, which lasted less than three years.
During that time, Fudge, 55, a former Kraft Foods senior executive with no previous agency experience, presided over a series of major account losses, including Burger King, Sony and Jaguar.
In July, she handed control of Y&R Advertising over to Hamish McLennan, the head of Y&R Brands in Australia and New Zealand.
"Fudge probably wanted to get out, but nobody seems to have tried very hard to keep her," a Y&R source said.
Fudge's fate is said to have been determined by her failure to revive the North American fortunes of Y&R.