Construction will start on site later this month and is due for completion in March 2016.
Sisk is believed to have beaten off competition from Willmott Dixon, Higgins and Ardmore to land the deal.
An industrial site on the corner of the estate was demolished during the summer to make way for the new homes.
Ten new blocks will be built, including one 20-storey block, while the remaining will range between 3-7 storeys.
Cllr Julian Fulbrook, Cabinet Member for Housing, said: “We are very pleased to have the skills and expertise of Sisk to help deliver our regeneration project at Maiden Lane.
“The new development will provide much-needed high quality new council rent and shared-ownership housing, which will help to address critical issues as overcrowding and improve the quality of housing in Camden.”
Mike Higgins, Director at John Sisk & Son Ltd, added: “We are absolutely delighted to be working with London Borough of Camden on this major regeneration scheme which will transform the neighbourhood.
“A key focus will be working with the community to ensure the scheme delivers a sustainable legacy.”