The developer has bought a stake in the site from Universities Superannuation Scheme (USS) for £41.5m.
British Land and USS are already joint venture partners developing the Whiteley Shopping Centre in South Hampshire.
Eden Walk currently has 276,000 sq ft of space containing 22 shops, three offices and a 697 space multi-storey car park.
The centre was built in 1968, extended in 1979 and refurbished in 2010, and is anchored by Marks & Spencer, Sainsbury’s, Boots and BHS.
British Land said it will now “act as development manager appraising opportunities to extend and enhance the centre in liaison with other key stakeholders, including The Royal Borough of Kingston-upon-Thames.”
Charles Maudsley, Head of Retail for British Land, said: “We are delighted to extend our successful relationship with USS and secure a key, strategic asset with extremely strong underlying fundamentals and significant development potential, increasing British Land’s exposure to the Greater London market.
“Kingston’s superb catchment and shopper profile offer huge potential and British Land has the ability, experience and the right strategy to deliver an exceptional world class town centre development.”