The law was supported by 193 lawmakers out of 249 present, with 56 voting against it.
"This is an important day for human rights," Prime Minister Alexis Tsipras told the chamber.
Tsipras said the bill gives same-sex couples "equal rights in life and death," terminating a practice of "backwardness and shame" for Greece.
The new law resolves property and inheritance issues, but makes no provision for the adoption of children.
Amnesty International hailed the move as a "historic step" but noted that lesbian, gay, bisexual, transgender and intersex (LGBTI) persons still faced hostility in Greece.
"Despite this first step, LGBTI people in Greece still live in a climate of hostility from which the authorities are failing to protect them adequately," said Gauri van Gulik, Amnesty International's Deputy Director for Europe and Central Asia.
"Physical attacks are on the rise, hate speech is common and goes unchecked by the authorities. Even displays of affection between same-sex couples are censored on television," van Gulik added.
Amnesty further pointed out that the law offers no gender recognition to transgender people.
Greece had been condemned for anti-gay discrimination by the European Court of Human Rights in 2013, after gay couples were explicitly excluded from a prior civil unions law in 2008.
"Instead of celebrating this, we should apologize to thousands of our fellow citizens," Tsipras said.
In addition to Tsipras' left-wing Syriza party, the bill was supported by another four parties.
However the nationalist Independent Greeks (ANEL), who are part of the governing coalition, voted against the motion.
"The Greek constitution protects motherhood. Is there motherhood in men?" asked ANEL lawmaker Vassilis Kokkalis.
Members of the Greek gay, lesbian and transsexual community had earlier staged protests outside parliament and the Athens cathedral.
"Love is not a sin," read a sign held by protesters as two young men dressed like priests kissed in front of the cathedral.
Greece was until now one of the last European countries where same-sex couples could not receive some kind of official recognition for their relationship.
The country's first two same-sex civil marriages held in 2008 were annulled by a court a year later under pressure from the Greek Orthodox Church, which officially frowns upon same-sex relations.
Lobbying by the church was also instrumental in excluding same-sex couples from benefitting from the 2008 civil union bill which modernized family law and aligned national law with EU rules.
A prominent Greek bishop this week described homosexuality as a "crime" and said "accursed" gays should be "spat upon."
source: interaksyon.com
