Southwark Council says it expects a "substantial capital receipt" from the sale of the former children's social services offices in Harper Road.
The buyer's identity has not been disclosed but the council has said that the new owner "proposes a residential development" for the 0.4-acre site.
"Southwark Council is committed to ensuring that we are securing maximum value for money for the residents of the borough," said Cllr Richard Livingstone, cabinet member for resources.
"Part of this work has included the accommodation review that we agreed in November 2010 that has resulted in reducing the number of buildings that the council operates from.
"One of the buildings identified for sale as part of that process was the former children's social services offices at Harper Road."
The council received more than 150 enquiries from prospective buyers.
• More details at www.harperroadse1.com