The politically left Pahor, in his first statement after the unofficial results of Sunday's voting were announced, called for national unity and said his win was "the beginning of something new, a new hope and new times," B92 reported.
Pahor gets a five-year term.
Danilo Turk, also of the political left, conceded defeat and did not offer a reason for his poor showing.
The runoff came while Slovenia experienced the largest demonstrations in its 20 years of existence. B92 said more demonstrations were planned across the country to protest what organizers called "corrupt elites" and poor social and economic conditions.
Unofficial results indicated about 40 percent of the eligible 1.7 million voters went to the polls.
"[Trust] in institutions must be rebuilt, while those institutions must earn it by diligently working in the common interest," Pahor said.