By Miriam Gottfried and Dave Sebastian

KKR & Co. agreed to buy the retirement and life-insurance company Global Atlantic Financial Group Ltd. for more than $4.4 billion, in a deal that would boost the private-equity firm's assets under management by more than one-third and help it dig deeper into a market rivals have been mining aggressively.

KKR, which already manages $26 billion in assets on behalf of insurance companies, plans to take over management of roughly $70 billion of Global Atlantic's assets. KKR's total assets under management would climb to $279 billion from $207 billion as of March 31, with the percentage of the firm's assets that are deemed permanent capital -- money that is particularly prized by private-equity firms because it doesn't need to be regularly replenished -- rising to 33% from 9%.

In buying a large chunk of insurance assets, KKR is following the path of rivals Apollo Global Management Inc. and Blackstone Group Inc. When the firms take over management of the assets, they help insurers in their aim to earn more money than they have to pay out to policyholders, a task that has become more difficult in an era of low interest rates.

Estimates put the assets of the global insurance industry at more than $30 trillion, KKR Co-President Scott Nuttall said on an investor conference call Wednesday. "It's an enormous market and in this low-rate world, we've been finding that insurance companies are looking for alternative investments within their portfolios."

Investors cheered the news, with KKR's shares up roughly 8% in midday trading.

Apollo, the original architect of the strategy, joined with former American International Group Inc. executive James Belardi in 2009 to build what would become Athene Holding Ltd. Financed by an investment from a publicly traded vehicle Apollo controlled, Athene bought up fixed-annuity assets on the cheap in the aftermath of the financial crisis and signed them over to the buyout firm to manage.

Apollo now manages $140 billion of assets on behalf of Athene and Athora Holding Ltd., a European insurance company it founded in 2014. That accounted for 44% of Apollo's total assets at the end of March and contributed the bulk of the $190 million in fee-related revenue the firm received from permanent-capital vehicles in the first quarter.

Apollo's credit business has ballooned as a result of the strategy, becoming the envy of its peers, and is now the industry's largest, with $210 billion in assets as of March 31.

Blackstone got the right to manage the assets of FGL Holdings Inc., formerly known as Fidelity & Guaranty Life, when a special-purpose acquisition company in which the private-equity firm invested bought the insurer in late 2017. In February, FGL said it was extending and enhancing its relationship with Blackstone in conjunction with a deal by Fidelity National Financial Inc. to buy FGL for $2.7 billion.

Closely held Global Atlantic has nearly $90 billion in assets and more than two million policyholders. The insurance company was founded in 2004 by Goldman Sachs Group Inc., where Global Atlantic Chief Executive Allan Levine served as chief executive for the investment bank's reinsurance group. It separated from Goldman in 2013.

Global Atlantic has a history of expansion through acquisitions, completing 20 reinsurance transactions covering about $27 billion in assets since its founding. KKR said it plans to continue to build the business through mergers and acquisitions.

Like Athene and FGL, the company focuses on fixed annuities, which pay owners a set amount of interest over the life of a contract. Insurers make money by earning more on the money handed over by buyers than they are required to pay out, making them attractive to private-credit managers.

KKR will pay the amount of Global Atlantic's book value as of the deal's closing through a combination of cash from the firm's balance sheet, proceeds from potential minority co-investors and the issuance of debt or equity. Global Atlantic's book value as of March 31 was about $4.4 billion, the companies said.

Global Atlantic shareholders, which include Goldman and its private-wealth clients, will have the opportunity to roll their investments into the deal. KKR said it initially expects to have about 60% economic ownership of the company.

Global Atlantic will remain a separate business under the leadership of Mr. Levine.

Write to Miriam Gottfried at Miriam.Gottfried@wsj.com and Dave Sebastian at dave.sebastian@wsj.com