Healthscope said the offer price would be reduced by any future dividends it pays to shareholders before the deal is complete.
"Whilst the board is of the strong belief that the company is well positioned to continue to deliver strong growth for shareholders into the future, the board determined that the relative certainty delivered by this cash offer at a substantial premium was in the best interests of Healthscope shareholders," Healthscope Chairman Linda Nicholls said in a statement.
The deal still requires Healthscope shareholder, court and other regulatory approvals.
Healthscope operates 44 private hospitals and has pathology facilities in Australia, New Zealand, Singapore and Malaysia.
The agreement ends a bidding process that had included multiple companies.
Media reports have identified one of the offers as having been from U.S. private equity firm Kohlberg Kravis Roberts & Co. U.S. hospital operator Tenet Healthcare Corp. in June dropped out of the bidding after it said information about its discussions with Healthscope was made public prematurely and caused its share price to tumble.A