The building is famous as the former home of Apple Records where the Beatles made their last public live appearance on the roof in January 1969.
The building has been sold to GHSR LLP and the deal will be finalised once Kier has completed refurbishment work.
The property was valued in Kier’s books on 30 June 2011 at £13.7m.
But Kier said “there has been, and will be, considerable works undertaken prior to completion at significant cost.”
The contractor added: “It is expected that these ongoing works and the conditions will be satisfied in order for completion of the disposal to take place by 31 March 2012.”
Kier has also raised £8.1m in cash from the sale of its investments in the West Berkshire and Hinchingbrooke Hospital PFI Projects. The deal equates to a £6.8m profit.
Kier will continue with a 27-year FM contract at Hinchingbrooke Hospital.