In May of this year, Philip Morris made a bid for Swedish Match of SEK 105 per share, or a total of SEK 161 billion.
On Thursday last week, the Americans raised the offer to SEK 116 per share.
The Swedish Financial Supervisory Authority gave the green light for the deal this summer.
With the European Commission's approval, which came on Tuesday after a six-week review of the takeover, comes a condition.
Philip Morris must sell the Swedish Match company SMD Logistics, because the company has a dominant position when it comes to the distribution of, among other things, cigarettes in Sweden.
Otherwise, the EU Commission believes, there is a risk that distribution prices will be raised and that competitors' products will be disadvantaged.