Remgro, a major shareholder of South Africa's Mediclinic, bought a 29.9 per cent stake from Cinven for 360 pence per share, equal to £432m.
Cinven has been gradually shrinking its holdings after it floated the healthcare company in July last year.
"This is an exceptional opportunity for us to gain a strategic investor who understands our business and growth ambitions as we develop our asset base to meet the significant capacity growth we expect for the UK private healthcare sector," Robert Roger, chief executive of Spire, said in a statement.
"We are investing in a growing developed market while also diversifying into an attractive new geography with a strong currency," Danie Meintjes, chief executive of Mediclinic, said.
"Both Mediclinic and Spire will benefit from collaboration through the sharing of knowledge and experience and improving cost synergies and efficiencies." Danie Meintjes, chief executive of Mediclinic, said.
Mediclinic is a South Africa-based private hospital group with operations in Southern Africa, Switzerland and the United Arab Emirates.
Both Mediclinic and Remgro have said they do not intend to make an offer to buy the whole of the company.