The Department for Transport and Department for Communities and Local Government has agreed to give the go-ahead to the scheme, nine years after its initial proposals.
The £3.5 billion project is yet to secure funding, but according to a Network Rail spokesman, it is unlikely that planning would have been granted if money was not on the horizon.
The green light will mean various buildings in the London Bridge area will be demolished to make way for the scheme.
Among them is a block by 19th-century architect Robert Smirke, who designed the British Museum, as well as Grade II-listed train sheds at the back of London Bridge Station.
Adam Wilkinson, of SAVE Britain's Heritage, said: 'This is the end of the line for our opposition to the works, and we're obviously very disappointed.
'It is a great shame they cannot retain the Smirke building, or the elegant train sheds at the back of London Bridge station.'
The construction of the scheme is likely to last for seven years.