The 41,700 sq ft (3,875 sq m) building - which is located immediately south of Euston Road and close to King’s Cross, St Pancras International and Euston stations - was constructed in the 1960s and comprehensively refurbished in 2008.
The deal will complete after Camden vacates the premises later in the year.
Lambert Smith Hampton was appointed to advise on the disposal last year.
Stephen Armitage, national head of the Public Sector team at Lambert Smith Hampton, said: “This is another example of a local authority asset managing its corporate portfolio to maximum benefit, enabling the release of significant value for recycling into front line services. We are delighted to have worked on this transaction, which raced to exchange of contracts within 6 weeks.
“The transaction represents a successful conclusion for Camden, and demonstrates the value of sound strategic advice in a fast-moving market.”
Lambert Smith Hampton works with over 250 public sector bodies and 170 local authorities, including 18 London boroughs.