Former owner Aviva Investors has sold its stake in the mixed-use complex for £470m.
The deal means planned construction work at 4 and 5 Kingdom Street on the site, which was on hold, will now go-ahead.
The development sites at 4 and 5 Kingdom Street have consent for around 355,000 sq ft of offices.
Designs by architect Allies and Morrison are at an advanced stage.
But British Land said: “It is our intention to add to, and improve, the existing consents.
“Subject to consent being received, we expect to commit to these developments and start on site towards the end of 2014.
“The expected cost to complete is around £180 million.”
Tim Roberts, Head of Offices, British Land, said: “Managing and developing large estates in London is what we do well.
“With the benefit of improving local infrastructure, the regeneration of Paddington as a whole, plus our ability to improve and complete the estate, I am confident we can take Paddington Central to the next level and in the process, deliver attractive returns.”