Japan Tobacco Inc. said Thursday it has agreed to acquire independent U.S. electronic cigarette company Logic Technology Development LLC.

Terms of the deal, which is expected to close in the third quarter, weren't disclosed.

The acquisition would give Japan Tobacco the third largest e-cigarette company in U.S. convenience stores with about a 20% market share, according to Nielsen data cited by Wells Fargo. It also would give Japan Tobacco a proven e-cigarette brand that it can push globally.

The deal is the third major acquisition of a U.S. e-cigarette brand by a big tobacco company. Altria Group Inc. last year acquired Green Smoke for $110 million, and Lorillard Inc. in 2012 acquired Blu Ecigs for $135 million. Reynolds American Inc. in 2013 launched its own brand Vuse, which leads the convenience-store market with about a 33% share. Blu is second with an estimated 22% market share.

Those brands account for an estimated $1.5 billion of the $3 billion e-cigarette market, according to Wells Fargo. The rest of the industry is dominated by large, refillable systems called vaporizers that heat liquid nicotine. Vaporizers and liquid nicotine, known as "e-liquid" or "juice," are primarily sold at so-called vape shops.

Adding Logic to its portfolio would make Japan Tobacco a player in the U.S. vapor market, which is projected to grow 30% this year. The company expanded its international tobacco business in 1999 when it acquired R.J. Reynolds international operations for $7.8 billion. More than 80% of its revenue comes from tobacco and cigarette brands it sells world-wide such as Winston, Camel and Benson & Hedges.

"With the Logic brand and its strong portfolio of products, the JT Group has a sizable participation in the largest and fast-growing U.S. e-cigarette market," said Masamichi Terabatake, Japan Tobacco International's executive vice president. He added that the company has "global ambitions to become the leader in emerging products" with Logic and the U.K.-based e-cigarette company E-Lites, which it acquired last year.

Logic was founded in 2010 by Eli Alelov and Howard Panes. The company specializes in rechargeable and disposable e-cigarettes known as "cigalikes" because they are designed to look like traditional cigarettes.

Japan Tobacco said it plans to retain Logic's management team, which includes President Miguel Martin, who previously oversaw sales at Altria. A spokesman for Logic declined to say if Mr. Alelov or Mr. Panes, who respectively serve as chief executive and chief operating officers, would continue to work on Logic's business after the sale closes.

Write to Tripp Mickle at Tripp.Mickle@wsj.com

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