BBH won the business after a pitch and is charged with relaunching the brand, which was first established in 1755, into the mainstream menswear market.
The company, which is based in Leicester and holds a Royal Warrant for its services to the Queen, claims to be Britain's oldest clothing brand. It is owned by Jon Hargreaves, the owner of Matalan, which is a BBH client.
BBH will develop a new identity and a launch campaign towards the end of this year. The agency, which will work closely with Stephen Reeds, the brand director at Wolsey, will also help to exploit the brand's sponsorship deals, such as its support for Henry Worsley's "Shackleton" South Pole expedition.
Jon Peppiatt, the deputy chairman of BBH, said: "This is an opportunity for us to develop a long-term partnership with Wolsey."