Kindred Healthcare said Tuesday that its board had agreed to be acquired in a $4.1 billion all-cash deal by two private equity partners and Humana.

Shares of Kindred, a Louisville-based hospital, rehabilitation and home health company, were down 5 percent in mid-morning trading after having jumped 10 percent early in the morning. Shares of Louisville-based health insurer Humana were down slightly.

The Wall Street Journal on Sunday had reported about advanced talks between the companies.

Kindred said in a press release that the $4.1 billion deal would include the assumption or repayment of net debt. According to its most recent quarterly filing, Kindred held long-term debt of about $3.3 billion.

Kindred provides health care services in nearly 2,500 locations in 45 states, employs 86,400 and generates annual revenue of about $6.1 billion. Humana employs about 27,000 and through three quarters this year generated revenue of nearly $41 billion.

Benjamin Breier

Kindred CEO Benjamin Breier said in a press release that the deal would transform home health care in America “by enhancing access to care and reducing costs for people living with chronic conditions.”

Humana CEO Bruce Broussard said the acquisition would bolster the insurer’s capabilities to focus on patients in the home “while delivering high-quality care in a low-cost setting.”

Under the terms of the deal, Kindred shareholders would receive $9 in cash for each Kindred share they own. That’s a premium of 40 cents over Kindred’s closing price on Friday.

Kindred would be split into two businesses: Kindred at Home would focus on home health, hospice and community care and would be owned 40 percent Humana and 60 percent by TPG Capital and Welsh, Carson, Anderson & Stowe. Kindred Healthcare, led by Breier, would focus on the company’s long-term acute care hospitals and inpatient rehabilitation facilities.

Humana, over time, would have the right to buy the remaining stake in Kindred at Home.

TPG, started and based in Fort Worth and San Francisco, operates 16 offices around the world and has $73 billion under management. WCAS, based in New York, invests in health care and technology and has raised and managed more than $22 billion. Its portfolio includes about 25 companies.

The parties said that the deal is subject to approval of stockholders and regulators. They said they expect the transaction to close during next summer.

This story has been updated.