Mays, currently a press director at ZenithOptimedia, will join The Mail on Sunday with the task of communicating its qualities to advertisers and strategic planners.
He will head three teams, including the client team, the strategy and planning team and the creative solutions team, comprising 23 executives.
This new structure is part of plans unveiled in August as The Mail on Sunday vowed to offer advertisers a more strategic approach.
Mays will report to Steve Atkinson, the deputy advertisement director.
Atkinson was promoted in August from the role of head of newspapers, part of a restructure that saw the departure of Chris Willis, The Mail on Sunday's head of magazines.
Simon Davies, the advertisement director at The Mail on Sunday, said: "This is a big investment for us and we're delighted that Stuart has decided to join us."