Confirmation of start of work cones after the secretary of state for transport Patrick McLoughlin signed off on the project, giving his final approval.
The line, from Kennington to Battersea via Nine Elms, is set to cost £1bn to build, with the main construction contract worth £500m to the Ferrovial Agroman Laing O'Rourke joint venture.
Two new stations will be constructed – one at the Battersea Power Station redevelopment and another at Nine Elms to the east, serving new developments such as the US Embassy and the redevelopment of New Covent Garden Market, as well as existing communities.
The new line is being funded entirely through contributions from the developments in the area that will benefit from the extension.
London Underground managing director Mike Brown said: “This vital new part of the Underground network will support and enable growth in an area that is rapidly developing. By 2020 we will have created over three miles of new tunnels and two brand new stations that will transform transport links to the area.”