The town hall will become the centre piece of a mixed-use development known as the SW2 Enterprise Centre.
The winning company will design and deliver refurbished council offices alongside new residential and commercial developments.
Part of the profit from the private development will be used to help fund the revamp of council offices.
Construction work is expected to last three years and up to six bidders will be invited to make up a shortlist with a bidders open day to be held on August 13.
Firms have until September 3 to register their interest in the scheme.
To register and to book a place on the open day contact London Borough of Lambeth, Rachel Willsher E-mail: SW2EnterpriseCentre@lambeth.gov.uk
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