SP Setia and Sime Darby have officially bought the 39-acre site on the south bank of the River Thames for £400m.
Local planning authority Wandsworth Council said the announcement was “potentially very good news”.
The power station opened in 1933 and generated power until 1983. It has become an icon of the London skyline and was used on the cover of Pink Floyd’s 1977 album Animals.
Part of the winning application includes a promise to build a new London Underground station on the Northern Line near the site.
Chelsea FC was one of 15 bidders, and planned to develop the station into a 60,000 capacity stadium.
Wandsworth Council leader Ravi Govindia said: “It’s important that this site and its iconic building are not left behind and that a developer is brought in who understands our vision.”