IA leader Mr Kleist said Greenlanders deserved the election result
The left-wing Inuit Ataqatigiit (Community of the People, IA) party has won Greenland's parliamentary elections, official results show.
The party ousted the Social Democratic Siumut Party, which has governed the territory for 30 years.
With all districts counted, the IA had nearly 44% of the vote and Siumut just over 26%, the election commission said.
IA will be the first party to govern the semi-autonomous Danish territory under an expanded home-rule agreement.
IA leader Kuupik Kleist told supporters celebrating in the capital, Nuuk: "Greenland deserves this."
Current Prime Minister Hans Enoksen had called the election early, after Greenland voters approved plans in November to give their government more powers.
He said he had wanted to give islanders the chance to decide who would be leading them into the "new era".
Under the new status, Greenlanders will be able to make decisions on most issues.
But the authorities will continue to negotiate with Denmark on defence and foreign affairs.
Correspondents say the polls were seen as a turning point in Greenland's path to partial independence from Denmark.