The decision to buy the site is part of SEEDA's urban regeneration drive.
Last year, it created the UK's first brownfield land assembly trust to buy and remediate packages of land in and around city centres with the intention of selling them on and reinvesting the proceeds to buy other contaminated land.
SEEDA has made an initial down payment of £6.5m for the 12.5 ha site with the balance to be paid in instalments until March 2007 as the site is developed.
Paul Hudson, SEEDA's development and infrastructure director, said: "Our immediate task is to discuss with Southampton council the detailed proposals for the redevelopment of the site and to commission all the necessary studies so that we can identify the best way forward."
SEEDA is also heading a taskforce involved in the £38m regeneration of Hastings and Bexhill in East Sussex.
The 10-year, government-funded plan aims to improve the area's infrastructure and build a series of mixed-use developments across the region.