The company, one of Japan's biggest insurers, said it would pay $70 per share and issue up to 250 billion yen ($2.4 billion) in new stock to help finance the deal.
The price is a 34 per cent premium on Protective Life shares when they closed on Friday in New York, before reports of the deal emerged.
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"As a result of the acquisition, the company's business composition in terms of premium income, profits and risk exposure will be more diversified globally, encompassing Japan, North America, and the Asia-Pacific region," Dai-ichi said in a statement.
"The group anticipates the acquisition to be a transformative event for (its) aspiration to become a 'global insurance group representing Asia', enabling us to accelerate growth and expand our business further," it added.
The buyout - which is expected to complete later this year or early 2015 - would be the largest acquisition of a foreign firm by a Japanese insurer, eclipsing the $4.7-billion takeover of US-based Philadelphia Consolidated by Tokio Marine in 2008.
Last month, Japan's Suntory Holdings said it had completed a nearly $16 billion purchase of the firm behind Jim Beam bourbon, creating one of the world's biggest high-end spirits makers and giving it a foothold in the major US liquor market.
That deal - which eclipsed previous foreign acquisitions by Suntory - was the third-biggest overseas takeover by a Japanese firm, after mobile carrier SoftBank's $21.6 billion buyout of US-based Sprint Nextel last year and Japan Tobacco's 2007 purchase of Britain's Gallaher for almost $19 billion.
Dai-ichi's announcement was the latest in a recurring trend for Japanese companies as they see their home market declining due to a shrinking population.
A strong yen in recent years also helped propel the shopping spree as overseas deals were relatively cheaper for Japanese companies, although the pace has slowed as the currency has sharply weakened over the past year.
Dai-ichi's Tokyo-listed shares, which dropped about 5.0 percent Monday on dilution concerns following reports of a possible deal, were up 0.41 per cent at 1,453 yen by the break today.
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