The board of Swedish Match recommended that its shareholders accept the bid of 106 Swedish kronor per share, nearly 40 percent above its closing share price on Monday, the companies said in separate statements.
The deal would total 161.2 billion Swedish kronor (15 billion euros).
Stockholm-based Swedish Match derives more than 65 percent of its revenue from smoke-free products, including chewing tobacco and the Zyn brand of nicotine pouches.
Philip Morris announced in 2016 a long-term goal to stop selling cigarettes and replace them with alternatives that it says are less harmful.
The US company sells cigarette brands such as Marlboro and Chesterfield in 180 markets outside the United States and has invested billions of dollars since 2008 in vapor products, oral nicotine and other “reduced-risk” products.
Last year it clinched a controversial takeover of British breathing inhaler manufacturer Vectura, despite fierce opposition from health campaigners and medical groups.
The group plans to generate at least $1 billion in annual net revenues from nicotine-free products by 2025.
Philip Morris and Swedish Match had confirmed the takeover talks on Monday following a Wall Street Journal report.
“We are pleased to announce this exciting next step in Philip Morris International’s and Swedish Match’s trajectory toward a smoke-free future,” the US company’s chief executive, Jacek Olczak, said in a statement.
“Underpinned by compelling strategic and financial rationale, this combination would create a global smoke-free champion — strengthened by complementary geographic footprints, commercial capabilities and product portfolios — and open up significant platforms for growth in the US and internationally,” he said.
Swedish Match chairman Conny Karlsson told AFP that the deal was a “good offer” for shareholders.
“It’s great to have the chance to broaden the distribution of our products, which can compete with cigarettes,” Karlsson said.
Swedish Match is also known for making cigars and “snus”, a form of snuff particular to Nordic countries.
The sale of snus, a moist powder tobacco originating from dry snuff, is illegal across the European Union, but Sweden has an exemption. It contains nicotine and comes in teabag-like pouches that are placed under the lip.
In 2012, Swedish Match said an associate to the EU’s then health commissioner had sought a 60-million-euro payment from the company to push for a proposed tobacco law that would lift the snus ban.
The firm filed a complaint with the European Anti-Fraud Office and the health commissioner, John Dalli, resigned from his post.
Dalli appeared in a Maltese court this year on charges of bribery and trading in influence over the lobbying scandal.
Swedish Match shares rose by almost nine percent to 103.50 kroner following the takeover bid.
Philip Morris, listed on the New York Stock Exchange, was up 0.6 percent to $99.47 in electronic trading before the stock market opened.