The building is currently let to the Department for Constitutional Affairs, which pays rent of £34/sq ft.
The deal is part of Land Securities' sale of its non-core assets that netted the firm less than expected, the commercial propertywebsite has suggested.
It claimed it was hoping to get £81 million, a four per cent yield, when it bought the building to the market in December 2007.
Real IS is also buying 14 Tothill Street, a 56,000 sq ft office near Parliament Square for £58 million from Gracemark.
Land Securities is set to de-merge. Rick Haythornthwaite, the new chairman of its retail arm, told the Telegraph: "It clearly has a high-quality estate which it is managing for value very well, and it is going to be in a very strong position."
