The Oasis Leisure Centre will be taken over by Moirai Capital Investments on June 1.
Moirai will refurbish the run-down centre with work starting during the summer to revamp the site and replace its glass dome.
Further plans include construction of an indoor ski slope at the site with work worth up to £65m in the pipeline for McAlpine and ISG who are working closely with Moirai.
Martin Barber, who is leading the Moirai development, said: “We are delighted to have reached agreement with the council, and to have exchanged contracts. The real work now begins.
“We are ready to press forward enthusiastically with the first phase, the refurbishment of the Oasis Leisure Centre.
“We have already plans in hand for the replacement of the Dome and the refurbishment of the changing accommodation.
“Over the coming 12 months, we shall be undertaking a significant facelift of the centre to ensure that it returns to a facility of which Swindon can be proud.
“In terms of the further developments on the other areas of the site, we shall shortly be able to make some significant announcements about our proposals to position Swindon as the major leisure and entertainment destination for the south-west.”
Moirai , under its X-scape brand, was behind the Milton Keynes, Castleford and Braehead indoor ski slopes.