The Mayor's office says that the Northern Line extension will reduce pressure on Vauxhall station and existing Northern Line services, in addition to boosting the area's economy.
It is expected that work on the line could begin by 2015, with services in operation by 2020.
A consultation on the plans is already underway.
More top news
Members of the RMT union will walk out in a row over the role of conductors, causing fresh misery for hundreds of thousands of passengers.
The five year long jail sentence of a London mother held in an Iranian jail has been upheld.
Barnet police are investigating four separate anti-semitic offences in the last two days