Preliminary results from the country's parliamentary elections shows the Conservative Party with 26.8% of votes, the best result for the party in 28 years.
Ms Solberg, who will be Norway's second female prime minister after Gro Harlem Brundtland, thanked the voters for a historic victory.
She said: "The voters had the choice between 12 years of red-green government or a new government with new ideas and new solutions."
Current prime minister Jens Stoltenberg, who has led Norway for eight years, conceded defeat, saying his Labour Party tried "to do what almost no one has done, to win three elections in a row, but it turned out to be tough".
The Conservative Party has said for the first time it is prepared to form a coalition government with the anti-immigration Progress Party which was the third-biggest party in the election.
This was the first parliamentary election since Anders Breivik, who was a member of the Progress Party before he lost faith in democracy, killed 77 people in 2011, most of them young people attending a Labour summer camp.