The law gives same-sex couples the right to wed and adopt children and comes after decades of campaigning by the LGBT community for marriage equality in the socially conservative country.
Greece is one of the first Orthodox Christian countries to allow such unions.
"This is a historic moment," Stella Belia, the head of same-sex parents group Rainbow Families, told Reuters. "This is a day of joy."
The bill was approved by 176 lawmakers in the 300-seat parliament and will become law when its published in the official government gazette.
Although members of Prime Minister Kyriakos Mitsotakis' centre-right New Democracy party abstained or voted against the bill, it gained enough support from the leftist opposition in a rare show of cross-party unity despite a tense debate.
"Its a very important step for human rights, a very important step for equality, and a very important step for Greek society," said 40-year-old Nikos Nikolaidis, a historian who joined a rally in favour of the bill ahead of the vote.
Recent opinion polls show Greeks are split on the issue. The powerful Orthodox Church, which believes homosexuality is a sin, has strongly opposed same-sex marriage, while many in the LGBT community believe the bill does not go far enough.
It does not overturn obstacles for LGBT couples in using assisted reproduction methods. Surrogate pregnancies will also not be extended to LGBT individuals, though the bill recognises children already born through that method abroad.
Elliniki Lysi, one of the three far-right parties represented in parliament, called the bill "anti-Christian" and said it hurts national interests.
Former Prime Minister Antonis Samaras, a New Democracy lawmaker, said: "Of course I will vote against it. The marriage of same-sex couples... is not a human right."
PROUD TO BE GREEK
LGBT groups rallied outside parliament. A banner read: "Not a step back from real equality."
"I'm very proud as a Greek citizen because Greece is actually - now - one of the most progressive countries," said Ermina Papadima, a member of the Greek Transgender Support Association.
"I think the mindset is going to change... We have to wait, but I think the laws are going to help with that."
Campaigners have been pushing for change for decades, often against the tide of the Church and right wing politicians. In 2008, a lesbian and a gay couple defied the law and married on the tiny island of Tilos, but their weddings were later annulled by a top court.
But there have been some steps in recent years. In 2015, Greece allowed civil partnership among same-sex couples, and in 2017 it gave legal recognition to gender identity. Two years ago it banned conversion therapy for minors aimed at suppressing a person's sexual orientation.
