The practice - the biggest in Britain - will work with the Duke of Westminster's vast development arm, Grosvenor, on the scheme.
The project has echoes of Liverpool's huge £750m Paradise Street redevelopment, in which the same development team is overhauling a massive swath of the city centre.
The Grosvenor and BDP team won the job against strong competition from Land Securities with Allies & Morrison, Capital Shopping Centres with Chapman Taylor, and Westfield.
The Crawley scheme covers a 10ha site in the northern part of the town centre. Proposals include the creation of new pedestrianised areas and squares. The significant profit-driver will be a series of retail developments, including new anchor stores.
An outline planning application is due to be submitted next year with simultaneous detailed planning for the new town hall. Subject to planning consent, the development could be complete by mid 2011.