The 93,000 square-foot property in Baker Street was bought from Irish developer McAleer & Rushe.
It will be developed as a mixed office and retail scheme which has already been given planning permission.
The company said it was confident that the market for office space in the capital was returning to health.
Tim Roberts, the company's head of offices said: “This is a great opportunity for British Land to buy into one of the limited number of prime central London locations with planning consent at an early stage in the recovery cycle.
“We are optimistic about the outlook for rental growth in the West End office market and expect to generate strong returns as we leverage our development expertise.”