This came a day after Georgia's pro-Western President Salome Zurabishvili - in conflict with the ruling Georgian Dream party - refused to sign the bill.
The bill is similar to Moscow's "gay propaganda" law, which also bans gender reassignment and annuls same-sex marriages performed abroad or on Georgian territory.
"In accordance with the constitution, today I signed the law on family values and protection of minors, which Salome Zurabishvili did not sign," Parliament Speaker Shalva Papuashvili wrote on Facebook.
The ruling Georgian Dream party pushed the bill through parliament last month. The vote heightened tensions ahead of crucial parliamentary elections on 26 October.
Papuashvili said the measure "is based on common sense, historical experience and centuries-old Christian, Georgian and European values, not on changing ideas and ideologies."
"The law protects the rights of all citizens," he added.
However, human rights groups and Western countries say the law is discriminatory and creates a dangerous environment for LGBTQ people.
Last month, a prominent Georgian transgender woman was stabbed to death, an attack that occurred during the push for the law.
The bill also comes in the wake of Tbilisi's recent adoption of a "foreign influence law" targeting NGOs, which sparked weeks of mass anti-government protests and condemnation from the West.
Critics accuse the ruling Georgian Dream party of moving closer to the Kremlin's orbit and threatening Georgia's EU membership bid. | BGNES
