
The agency, founded by Jason Frost, the former chief executive of Publicis Blueprint, and Craig Smith, Marketing's former editor, won the business following a competitive pitch.
In February, Publicis Blueprint was forced to resign some major accounts, as it had struggled to get a financial return on its third-party ad model.
It is understood that Debenhams is remunerating Frost Publishing with a fee, although the magazine will continue to carry third-party ads.