Doncaster Council said in February that Essex-based Runwood Homes was the preferred bidder to take over management of all of its homes.
The council previously planned to shut the sites and move residents into privately-run homes.
Runwood Homes said it planned to improve the living environment and increase the number of beds on offer.
The council has said it needs to save £70.5m by 2017. It has already saved £93m since 2011.
Campaign group Caregate, which had opposed the planned closures had handed in a petition with more than 20,000 signatures in 2014.
In a statement the company said: "We will be making new investment in the homes and there are plans to improve the living environment and increase the number of beds on offer in a modernisation programme over the next five years.
"The vast majority of residents will continue to be referred by the council, at their agreed fee rates. Respite services will also be offered.
"Runwood is a company that is new to the Doncaster area and we are keen to work collaboratively with relevant third sector organisations in understanding and responding to community needs."
Seven council-run care homes earmarked for closure to save £1.9m have been taken over by a private company.