The Sumitomo Life Insurance Company of Japan said on Tuesday that it had agreed to acquire Symetra Financial Corporation, an American provider of insurance and financial products, for about $3.8 billion.

The deal is the latest by a Japanese insurer seeking to expand its operations into the United States, the world’s largest insurance market, as an aging Japanese population is expected to cut into results.

Symetra would give Sumitomo Life its first real foothold in the United States.

Under the terms of the deal, Symetra shareholders will receive $32 a share in cash, and a special dividend of 50 cents a share. The deal represents a 32 percent premium to the company’s average share price over the 30 days that ended Aug. 5.

“We are enthusiastic about the opportunity to acquire Symetra’s dynamic business and believe that a transaction will be mutually beneficial and will create significant value for both Symetra and Sumitomo Life,” Masahiro Hashimoto, the president and chief executive of Sumitomo Life, said in a news release.

Mr. Hashimoto added that the acquisition would lift and diversify the company’s operations overseas, and would “enhance our financial and earnings foundation.”

Founded in 1957, Symetra, based in Bellevue, Wash., provides annuities, life insurance and employee benefits. It posted revenue of $2.18 billion in 2014 and has about 1,400 employees.

“This transaction will bring compelling strategic and financial benefits for Symetra, including providing a substantial cash premium to our shareholders,” Thomas M. Marra, president and chief executive of Symetra, said in a news release.

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