It will now keep a greater share of revenue from its natural resources, although much of the oil, gas, gold and diamonds that it holds has been inaccessible because of the Arctic ice that covers most of the land mass.
US scientists believe Greenland's northern tip is especially rich in oil and gas and they say global warming could actually help unlock the untapped wealth and provide a solid foundation for an independent economy.
Home to the US Thule radar base, Greenland depends on Danish subsidies, which account for two-thirds of the its economy.
Greenland became a colony of Denmark in 1775, and was a Danish province from 1953-1979.
Even after the adoption of self-rule, however, Denmark will still have the final say in defence and foreign-policy matters.
|Margrethe described the handover of the self-rule documents 'a big moment for me' [AFP]
Queen Margrethe of Denmark and Lars Loekke Rasmussen, the Danish prime minister, attended Sunday's celebrations in the capital, Nuuk, dressed in Greenlandic national costumes.
"This is a big moment also for me to hand over these self-rule documents to you and therefore to the Greenlandic people," Margrethe told Josef Motzfeldt, the speaker of Greenland's parliament.
Kuupik Kleist, Greenland's prime minister, who formed a coalition cabinet earlier this month, has promised to focus on social problems.
His party, the Inuit Ataqatigiit, won 44 per cent of the vote in the elections of June 2, taking 14 of the 31 seats in the parliament.
Kleist's party ousted the Social Democratic Siumut party, which had been in power in Greenland since 1979.