Terra Firma, chaired by Guy Hands, will acquire more than 500 UK homes and 30,000 staff through the sale. Four Seasons chairman Geoff Westmore said the company would be left with less debt and a stable financial base.
The company has been controlled by RBS since a debt-for-equity swap in 2009 which saw the bank take a 40% stake in return for help tackling its huge debts.
Unison, which represents many care workers, warned against a drive to maximise profits at the expense of staff training or wages.
Ranald Mair, chief executive of Scottish Care, said he expected the move would be positive for the sector.
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