The reinsurance arm of Brookfield Asset Management Inc. has agreed to buy American National Group Inc. for about $5 billion, the companies said.

As part of the deal, American National stockholders will receive $190 a share in cash. That represents a roughly 10% premium to the company’s closing price Friday of $172.80.

The Wall Street Journal reported earlier that the companies had reached a deal.

Assuming the deal is completed, American National will be wholly owned by Brookfield Asset Management Reinsurance Partners Ltd. , which spun out of the Canadian investment giant in June to become a publicly traded entity. (It is still affiliated with Brookfield Asset Management.) Brookfield said it plans to keep American National’s headquarters in Galveston, Texas, and maintain its operational hubs around the country.

American National, which has just under $30 billion in assets, provides life insurance and annuities as well as health, property and casualty and credit insurance and pension products.

With interest rates near historic lows, insurance companies have increasingly sought higher yielding alternatives to plain-vanilla corporate and government bonds to invest the cash they generate from customer policies. Private-equity firms with big credit businesses have jumped at the opportunity, building platforms that offer insurers a raft of tailor-made investment products.

For Brookfield’s reinsurance arm, which manages about $15 billion, American National will provide a sizable platform from which to bulk up. Brookfield Asset Management’s big real estate, infrastructure and renewable-power arms—in total it manages more than $600 billion in assets—help the reinsurance business source debt investments that are ideal for insurers because they are generally long-term in nature.

At an investor day last September, Brookfield Chief Executive Bruce Flatt said insurance could eventually be a $100 billion to $200 billion business for the firm.

The frenzy among investment firms to amass insurance assets has reached a fever pitch in recent months, with Blackstone Group Inc., Apollo Global Management Inc. and KKR & Co. all announcing big transactions.

Some firms, such as Blackstone, have preferred to take small stakes in insurers and ink deals to manage their assets. Others, including KKR and Apollo, a pioneer in insurance investing, have preferred to own the insurance companies outright.

Brookfield has done a bit of both. In October it announced a partnership with American Equity Investment Life Holding Co. , agreeing to reinsure up to $10 billion of fixed index annuity liabilities and make a 19.9% equity investment in the company. The firm, which has a sizable balance sheet, is likely to continue to put it to work in future deals.

Write to Miriam Gottfried at Miriam.Gottfried@wsj.com and Cara Lombardo at cara.lombardo@wsj.com