There will be no First Capital Connect or Southern trains calling at the station until 1 September.
The closure is part of the £6.5bn Thameslink programme, which aims to improve north-south travel through the capital.
Nicky Hughes from Network Rail said the redevelopment of London Bridge was a “huge challenge”.
“London Bridge is one of the country’s busiest stations and we’re rebuilding it piece by piece to transform north-south travel through London,” he said.
The disruption is likely to affect up to 50,000 commuters every hour who normally travel into the station on First Capital Connect and Southern services.
There will also be no direct trains to Gatwick or Luton airport stations from London Bridge.
However, London Bridge Underground station will be unaffected.
Network Rail has urged commuters to check their routes before they travel.
Simon Blanchflower, major programme director for the Thameslink programme, said the station was being rebuilt in stages.
“We started earlier this year and we closed certain platforms and rebuilt those, he said.
“We are at a stage where we are reopening two new platforms – 12 and 13 – and closing the next two – 10 and 11.
“To do that we have got to have a closure while we carry out the next phase of the work and also to do the necessary track work and signalling alterations that lead up to the station.”
The Thameslink Programme will see the size of the concourse at London Bridge railway station expanded and the number of trains to and through central London from the south east will also increase.
The project should be completed by 2018, Network Rail said.