The deal marks the latest instance of consolidation in a global seafood industry that analysts say has been in flux over the past few years, as companies change the way they manage supplies and costs to better cater to shifting consumer demand.
The transaction is likely to be completed in the second half of next year, subject to approval from U.S. antimonopoly authorities, said Thai Union, whose clients include Wal-Mart Stores and Costco Wholesale.
Thiraphong, whose company has operated in the U.S. for over 17 years, said he expected a "positive response" from the authorities.
But Thai Union may have to sell U.S. assets to win antitrust approval, said a person familiar with the transaction, who asked not to be identified because of sensitivity of the deal.
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Thai Union's Chicken of the Sea is the third-biggest tuna brand in the U.S. behind Bumble Bee. The top brand, Starkist, is owned by South Korea's Dongwon Industries.
Bumble Bee is the largest canned tuna and sardine producer in North America, with brands including Brunswick and Sweet Sue. It is owned by pan-Atlantic private equity firm Lion Capital, which bought the seafood maker from another private equity firm for $980 million in 2010.
It has annual sales of about $1 billion and estimated EBITDA of $145 million for 2014. Its purchase should boost Thai Union's sales next year to $5 billion from $4 billion, Thiraphong said.
The transaction is valued at 8.6 times Bumble Bee's 2014 estimated EBITDA, Bumble Bee said in a separate statement.
The acquisition would be Thai Union's third this year after the purchase of Norwegian canned fish producer King Oscar and French smoked salmon supplier MerAlliance. For further expansion, analysts said Thai Union's rising debt means the company would need to sell shares to raise capital.
Thai Union is open about its funding options to bring down its debt-to-equity ratio, which will rise after the Bumble Bee purchase to 2.0 times, or double the company's target, Thiraphong said.
But the acquisition should boost Thai Union's 15 percent to 17 percent gross margin, Thirapong said, as Bumble Bee's margin is more than 20 percent.
Shares of Thai Union closed down 3.5 percent after Friday's Bumble Bee announcement compared with a 0.2 percent decline in the benchmark index.
Thiraphong, 49, is the eldest son of Thai Union co-founder and chairman Kraison Chansiri, and took over as president when he was 30.
Kraisorn was born in Guangdong province, China, and started the business 37 years ago with a tuna cannery in the Thai province of Samut Sakhon, southeast of Bangkok. Tuna now makes up 47 percent of sales, with shrimp 24 percent and the rest from sardines, salmon, pet food and other products.
As well as Thailand and the U.S., Thai Union has been active in Europe since the 2010 purchase of MW Brand.
For its latest acquisition, Thai Union has hired UBS as adviser while Bumble Bee is being advised by Morgan Stanley and Rothschild.
Thai Union is financing the purchase with the help of a one-year bridge loan from Bangkok Bank and Siam Commercial Bank, executives from the two banks said.