The works are part of a major £20m project which Network Rail says will improve reliability and safety for train users.
Some 1.8km (1.1 miles) of track are set to be laid and 16 sets of switches and crossings, which allow trains to move from one track to another, installed between Charing Cross and Waterloo East, replacing rail equipment that has been used for 36 years.
The ends of the platforms at Charing Cross nearest to Hungerford Bridge will also be rebuilt with new foundations. These are currently subsiding, and the concrete surfaces are deteriorating, according to Network Rail.
Waterloo East will see upgrades to track drainage in order “to maintain track quality and a smooth ride at full line speed for passengers”.
The three-week closure will also allow engineers to make structural repairs to Hungerford Bridge, which dates back to 1864 and takes the railway over the Thames and provides two footbridges for pedestrians.
Network Rail says recent faults on the line have “caused over 21,000 minutes (350 hours) of delays to customers” and “completing the work in one extended closure will avoid a much longer period of repeated weekend disruption”.
Southeastern told BBC Radio London the work is being carried out over the summer because passenger numbers are 20% down compared with the rest of the year, and it would otherwise take 60 weekends of closures to complete the same amount of work being undertaken.
