TeamHealth, a U.S. hospital staffing provider, has been the target of activist funds including Jana Partners.
Blackstone will pay TeamHealth shareholders $43.50 per share held, a premium of about 18 percent to the stock's Friday close.
TeamHealth's shares rose to $42.45 in premarket trading on Monday.
The deal, expected to close in the first quarter of 2017, would allow TeamHealth to cope with pricing pressure as a private company, amid a wave of consolidation.
The U.S. physician services industry has been rapidly consolidating to counter rising administrative costs due to President Barack Obama's Affordable Care Act and the desire to offer a broader array of services to hospitals.
Following its rejection of Amsurg's offer, TeamHealth in November acquired smaller peer IPC Healthcare for $1.6 billion.
Knoxville, Tennessee-based TeamHealth, which offers outsourcing services, including emergency medicine, anesthesiology and ambulatory care, to hospitals and physician groups, had outstanding debt of $2.47 billion as of June 30.
Reuters earlier this month reported Blackstone was the lead bidder for TeamHealth, citing sources.
Team Health agreed in March to add three directors to its board following a deal with Jana, which had criticized its "missteps in critical areas including capital allocation, strategy and governance."
Goldman Sachs is the lead financial adviser and Citi the co-financial adviser to TeamHealth, while Simpson Thacher & Bartlett is the legal counsel.
Band of America/Merrill Lynch is Blackstone's financial adviser, while Kirkland & Ellis and Ropes & Gray are its legal counsel.