Reddy, 47, is credited with helping to develop DDB's strong print credentials, which saw the agency secure awards in nine categories at the Campaign Press Awards in March.
At McCann, Reddy will be charged with overhauling the agency's visual output, including its image. He will work alongside Frank Leiberman, who was enticed out of retirement earlier this year to be the executive head of TV.
Campbell called Reddy's appointment a "fantastic coup".
"Mark's in charge of everything to do with the still image - from the ads and the brand to the coffee cups," he said. "Without question, he's the best head of art in the business, in this country."
Reddy said: "Increasingly, big international agencies need to re-evaluate the visual language of their work."
Reddy studied graphic design at the Central School of Art & Design. He began his advertising career at Ogilvy Benson & Mather in 1975.
In 1977, Paul Arden hired him to the London Advertising Partnership (later Colmans). He had spells at Holmes Knight Ritchie and Saatchi & Saatchi before joining Doyle Dane Bernbach in 1986. His work includes ads for Volkswagen, Black Bush Whiskey and Heals.