In a statutory direction issued by the mayor, Livingstone is demanding that both TfL and the LDA carry out site clearance, demolition and decontamination before the new Olympic Delivery Authority takes over running the multibillion-pound project.
The authority will begin operating fully early next year once the London Olympics Bill officially becomes law.
Meanwhile, Livingstone claims he has also received 'clear assurances' of government funding, to help deliver all the projects. It is understood the money will come both from the Public Sector Funding Package agreed between the mayor and the government and from other central funds.
The mayor said: 'My direction to TfL and the LDA paves the way for them to deliver all the early work to prepare for the Olympic and Paralympic Games and will ensure this work is fully under way well in advance of the establishment of the Olympic Delivery Authority.
'Together with the government's reassurance that guarantees all the funding for these projects, we are sending out a strong message that the work to prepare for a truly exceptional Games in London in 2012 has begun.'
Olympics minister Tessa Jowell said: 'Once again, within 50 days of London winning in Singapore, there is more proof that all those responsible for delivering the world's greatest event are doing just that - delivering.
'[Now] these announcements signal that the work is under way on the Olympic Park and the infrastructure improvements which are vital to a successful Games in seven years' time.'