Mudge, the former director of Saatchi & Saatchi's in-house media operation, had been at Walker for a year and has left to pursue other interests.
He left Saatchis when the department was axed last year and joined Walker as a managing partner five months later.
Varley is a well-known media figure with a career spanning 20 years. He has previously worked with the Walker founding partner Phil Georgiadis at WCRS during the 80s. He joins from the screensaver media agency Oxigen, which he founded in 2000.
Christine Walker, a founding partner of Walker, said: "Charlie has a wealth of experience running big and demanding client accounts both in the UK and internationally. We're delighted that his timing fitted with our search for a new Dixons media head. He'll bring a fresh perspective to our business, particularly with the breadth of his commercial experience.
Our entrepreneurial culture, combined with the challenge of the Dixons Stores Group brief, was exactly what he was looking for."
Varley added: "To be back at the sharp end of media, as the champion of such a huge account across all media channels, is just what I wanted to do."