The Bhs agency appointment is being seen as a key factor in Green's expected declaration of war on Marks & Spencer after the failure of his takeover bid.
Green has said he will not fight M&S on price but will promote Bhs as offering a combination of quality and value. Budgets have yet to be finalised. M&S spends £25 million through Rainey Kelly Campbell Roalfe/ Y&R, although a substantial part of that spend is on food advertising.
Burton, which has up until now created all of its advertising in-house, is currently in discussions with several agencies.
Separately, Dorothy Perk-ins, one of Arcadia's women's fashion retailers, has awarded its creative advertising account to Grey London.
The agency scooped the business following a pitch involving Delaney Lund Knox Warren & Partners, Ogilvy & Mather, HHCL/Red Cell and Euro RSCG London.
The first work is expected to break in the autumn. Carat, which handles the media for the whole of the Arcadia Group, remains unaffected by the reviews.