The current Bankside House residence has 595 bed spaces and occupies a 1950s building originally used as ancilliary offices for Bankside Power Station.
The LSE took over the building in the mid-1990s.
This month the LSE announced that it has selected the development arm of Bouygues UK (Linkcity), working in consortium with Equitix, to provide investment and develop plans for the new residence to accommodate up to 2,000 students.
"We are excited to be working with Bouygues UK and Equitix on this project," said Julian Robinson, LSE's director of estates.
"This new building will form a key part of the LSE brand and identity.
"We will be looking for an exemplary piece of civic architecture which is affordable for all LSE students, focuses on environmental sustainability, health and wellbeing and offers an outstanding student experience."
Oliver Campbell, development director at Linkcity, said: "In line with LSE’s values, we will be putting climate and diversity at the heart of this project in order to deliver a vibrant, sustainable and truly inclusive space for students coming to live and study at LSE from across the world.
"We are delighted to been named preferred student accommodation partner and together with our partner Equitix, with our large portfolio of student accommodation across the UK, we’re excited to get started on this project for such a highly-revered and forward-thinking university."
In 2021 the LSE argued against Southwark Council's proposal to use its new planning policy document to protect the background of the view of Tate Modern from the Millennium Bridge, which it said would constrain the future redevelopment of Bankside House.
The Government-appointed inspectors who examined the Southwark Plan concluded: "Whilst it is not a listed building, the Tate Modern is an iconic building and sensitively managing the scale, massing and height of new development within the context of this landmark building through the proposed borough view is justified."
A planning application for the redevelopment of Bankside House is due to be submitted to Southwark Council in early 2025, and if approved, the development could be ready to welcome students in 2030.