More than 75% of Greenlanders have voted for self-rule in a referendum that could pave the way towards independence from Denmark.
At present, Greenland relies on subsidies from Denmark to sustain its economy.
Under the new arrangement, due to take effect in June next year, the Arctic island will take a greater share of its annual oil revenue, and Greenlanders will be treated as a separate people under international law.
If the proposals are enacted, Kalaallisut would become the official language, instead of Danish.
The plan would also see Greenland becoming less reliant on subsidies from Copenhagen. Currently these provide 30% of its gross domestic product.
Greenland would also take control of police, courts and coastguard, and have some say in foreign policy.
The BBC reports the vote could be a major step towards independence for the island of 57,000 people. About 50,000 of the population are native Inuit.
Hans Enoksen, the head of the local government in the Danish self-governing territory, thanked Greenlanders for "this overwhelming result" on Tuesday.
"The tears are running down my cheeks," said an emotional Mr Enoksen.
Final results showed that 75.54% voted in favour, while 23.57% said no - in line with predictions before the vote. Turnout was 71.96%.
Greenland gained self-rule in 1979, after previously being a colony and then a province of Denmark.
In 1985, the island left the European Union to avoid subjecting its fishing grounds to EU rules.