The site was sold to the house builder for around £150m.
Murdoch paid £300,000 in the 1980s for the 15-acre plot, which was put on sale last September after the closure of The News of the World.
News International had previously been planning to redevelop the site.
The Times, The Sunday Times and The Sun have since moved to the adjacent 550,000 square feet site at Thomas More Square, owned by Land Securities.
Barratt Developments and Cooper Group had also expressed interest in the site last year, which was one of London’s largest property plots on the market.