The offer, which was the consortium's fourth after the earlier ones were rejected by Mediclinic's board, values the company at £6.1bn ($7.41bn), Remgro and Mediclinic said in a joint statement.
Mediclinic is South Africa's third biggest operator of hospitals, and billionaire tycoon Johann Rupert's Remgro already owns up to 45% of the company.
Remgro, an investment company with operations spread across financial services, consumer products, infrastructure and healthcare, had been under pressure from investors and shareholders to unlock value and simplify the group structure.
Its plan to buy out Mediclinic is part of those efforts.
Mediclinic had dragged on Remgro's earnings as the hospital chain was hit by the Covid-19 pandemic and revenue from surgeries and other procedures dropped.
However, it has largely returned to normal operations and analysts had said the time was ripe for Remgro to unlock value in the company that could benefit shareholders.
Shareholders of Mediclinic will receive 504 pence in cash for each share of Mediclinic, a premium of 23% from the day before the final offer was made in early June, the companies said.
Mediclinic also has operations in Switzerland and the Middle East and is listed in the UK and South Africa. If the offer is approved by shareholders, Mediclinic will be delisted and held as a private company by the consortium, they said.
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