Though same-sex couples have been able to enter into legal partnerships since 2010, the legislation limited relationships and has since been deemed discriminatory, according to court documents seen by CNN.
The distinction between marriage and registered partnership cannot be maintained today without discriminating against same-sex couples....
Helmut Graupner, a lawyer for the two women who brought the case, wrote in a Facebook post that "today is a truly historic day".
"Because the separation into two legal institutions expresses that people with same-sex sexual orientation are not the same people with different sexual orientation".
"The judges ruled that banning same-sex couples from civil marriage is a violation of the fundamental principle that people are entitled to be treated equally, and that the state is not allowed to discriminate against people based on their personal characteristics", said Boris Dittrich, the lesbian, gay, bisexual, and transgender (LGBT) rights advocacy director at Human Rights Watch.
Many western European countries have introduced marriage equality.
Sana'a streets empty as Saleh's forces try to take capital from Houthis
Abdel-Malek al-Houthi, the leader of the rebels, called on Saleh to " show more wisdom and maturity " in a separate statement. Saleh's supporters managed on Saturday to seize control of several embassies and government buildings from the Houthis.
The conservative People's Party (OVP), who's leader Sebastian Kurz is expected to be sworn in as chancellor next month, said it will accept the ruling.
"Now there is equal treatment for something that's not equal", Herbert Kickl, the party's secretary-general, said in a statement. A marriage between women and men needs protection as only these partnerships can create children, he said. The Netherlands was the first country to approve marriage equality; same-sex couples have been marrying there since 2001.
The Homosexual Initiative Vienna (HOSI) welcomed the court's decision.
Constitutional courts in South Africa, Colombia, and Taiwan have also ruled that a ban on same-sex marriage in unconstitutional.