Prudential of Britain said Monday that it had agreed to buy American International Group's life insurance business in Asia in a deal valued at $35.5 billion. The sale of American International Assurance, which is based in Hong Kong and is commonly known as A.I.A., would lead to the biggest repayment yet toward the more than $180 billion that the U.S. government has invested in A.I.G. as part of a huge series of bailouts. The Federal Reserve Bank of New York, which holds preferred shares in A.I.A., would receive the first $16 billion in proceeds from a sale. With a takeover of A.I.A., Prudential would become the indisputable leader in Asia. Prudential said the combined group would be the leading life insurer in Hong Kong, Singapore, Malaysia, Indonesia, Vietnam, Thailand and the Philippines and the leading foreign life insurance business in China and India. A 162-year-old company — which is not related to Prudential Financial in the United States — the British Prudential already draws a large part of its revenue from Asia, with more than 11 million policyholders in 13 markets. “We are combining the two strongest international life insurers in Asia,” Tidjane Thiam, chief executive of Prudential, said in a conference call Monday to announce the deal. Acquiring A.I.A. accelerates a strategy outlined by Mr. Thiam to increase the firm's revenue in Asia sharply. The region is considered one of the fastest-growing markets for life insurance, thanks to a culture of saving and increasing affluence in many countries. “Transformational is an overused word,” Mr. Thiam said, “but this deal is transformational.” He noted that in 2008, 44 percent of new profit for Prudential came from Asia; if A.I.A. and Prudential had combined in 2009, the figure would have been 60 percent. That geography, he said, promises “sustainable growth for years to come.” Prudential said that the new company would assume the name Prudential, have headquarters and be incorporated in Britain and be traded on the London Stock Exchange with American Depository Receipts traded on the New York Stock Exchange. That said, the A.I.A. brand is not set to disappear. “We like good brands and we tend not to kill them unnecessarily,” Mr. Thiam said. “A.I.A. is a strong brand.” Once the deal is complete, the company said, it intends “in due course” to seek a dual primary-listing on the Hong Kong Stock Exchange. “This transaction offers the opportunity to bring together two leading companies, positioning the combined group to capture the future growth opportunity in Asia,” Prudential said. Under the terms of the deal, Prudential would pay about $25 billion in cash and about $10.5 billion in a combination of stock, preferred shares and convertible preferred shares. The company said it would obtain the cash for the deal through a $20 billion rights issue and $5 billion in senior debt. The rights issue must be approved by shareholders, and the deal faces other regulatory approvals. Prudential said it anticipated that the rights issue would take place in May and that the transaction would close in the third quarter. Several analysts downgraded Prudential shares on Monday. “It's going to be enormously dilutive,” ING analyst Kevin Ryan told Reuters, speaking of the rights issue. “No one knows exactly what A.I.A. contains or how profitable it is, or how it overlaps with Pru's existing businesses.” Prudential first approached A.I.G. last year, but it was rebuffed because its offer was too low, according to people briefed on the matter.