With voters turning their backs on the country's center-left government, Solberg, whose nickname is "Iron Erna," will be Norway's first Conservative prime minister since 1990, The New York Times noted.
It will be up to Solberg to assemble a ruling coalition, which the newspaper said may include an anti-immigration party.
"We will give this country a new government," Solberg said following Prime Minister Jens Stoltenberg's concession.
With 97 percent of the votes tallied, Stoltenberg's coalition appeared to have garnered only 72 seats to 96 for Solberg's Conservatives Progress and two small center-right parties, the Times said.
Prior to the vote, Solberg had said she was so confident of victory, she had already ordered a celebratory cake, Norwegian daily VG reported.
"I am quite sure that there will be a right-wing majority and a right-wing government," Solberg told Aftenposten.
"I do not think we will get in the 30s. I don't think any of the parties will," Solberg told Dagbladet newspaper.