MPs in the country, which has a population of 57,000, voted to adopt Danish legislation on the issue.
Two MPs were absent, but none voted against the measure.
The new measure will now scrap Greenland’s domestic partnership laws, adopted from Denmark in 1996.
The bill to make the changes to bring Greenland in line with Denmark, which legalised same-sex marriage in 2012, was announced in February.
Going into effect on 1 October 2015, the new law also grants adoption rights to same-sex couples, say reports.
Greenland in 2008 introduced discrimination protection for gay people, and in 2010 held its first gay pride event.