The agency beat Hurrell and Dawson and Isobel to win the business, in a pitch overseen by Sue Clague, commercial director of the hosiery brand's owner, Courtaulds Legwear Brands.
The appointment is part of a wide-ranging overhaul of the ailing brand, which has struggled to insulate itself from the effects of a declining market.
With an overhaul, the brand is expected to develop into new categories and PR agency Exposure, which has led Pretty Polly's marketing for the past three years, is expected to work closely with BMB.
The move reunites BMB co-founder Trevor Beattie with Pretty Polly, following a successful partnership in the mid-90s.
In 1996, when at TBWA\, Beattie famously created a 64-sheet poster, which required outdoor billboards to be turned on their ends to accommodate a 35-foot-high pair of legs.
The ad was one of the many iconic ad campaigns for the brand. Other celebrated Pretty Polly campaigns included an ad photographed by David Bailey which featured model L'Wren's legs as the hands of a clock.