"We have to be a little cautious, but it looks as though we will have a non-socialist majority," she told a rally of supporters chanting "Erna! Erna!" as confetti and streamers were dropped on the crowd.
Her Conservative Party, along with its anti-immigration junior coalition partner the Progress Party and two other centre-right allies, were on track to win a slender majority of 89 of the 169 seats in parliament, with 95 percent of votes counted.
The opposition, headed by Labour leader Jonas Gahr Støre, was seen taking 80 seats.
Store, a 57-year-old millionaire who has previously served as the country's foreign minister, conceded defeat and wished his rival well.
"This is a big disappointment for Labour," he told supporters, after results showed his party would lose six seats yet remain the largest in the country.
"Our goal was to give Norway a new government. We knew it was going to be close, and it was close. But as it looks now it wasn't enough to replace a Conservative-Progress Party government with a Labour government," he said.
Solberg's Conservatives meanwhile lost seven seats.
The election outcome hinged in great part on whether Solberg's small centre-right allies, the Liberals and Christian Democrats, would manage to break a key threshold in the vote.
Taking more than four percent of ballots translates into extra seats in parliament. Both parties long hovered around that mark, but were seen surpassing it.
The results confirmed opinion polls which had predicted an extraordinarily close race in "the world's happiest country".
Solberg's re-election marks the first time in more than 30 years a Conservative prime minister has won a second straight term.