The new law, which was approved by a two-thirds majority vote Wednesday, also makes the adoption process easier for same-sex couples and makes lesbian couples eligible for state-funded fertility drugs, Aftenposten reported.
"I am extremely pleased that we managed to get this last stage passed. Now we have to tackle the prejudice which still exists in society," Norwegian Finance Minister Kristin Halvorsen said.
Conservative opponents argue the law compromises the institution of marriage and could cause problems for children of same-sex couples.
Making fertility treatment available to lesbian couples is the most debated part of the legislation, the report said. Denmark, Sweden, Finland and Great Britain currently offer the treatment.