The State Election Commission released preliminary results late Sunday showing the referendum passed with more than 65 percent of the votes cast, the Croatian news agency HINA reported.
The BBC reported a government official confirmed the country's Constitution would be changed accordingly.
About 90 percent of Croatia's 4.4 million citizens consider themselves Roman Catholics and the church had urged them to vote "yes" on the referendum, the British news network said. Two-thirds of the members of the Croatian Parliament also had supported the ban on gay marriage, though some political leaders, including President Ivo Josipovic and Prime Minister Zoran Milanovic, and human rights groups had called for its defeat.
"The referendum result must not be the reason for new divisions," Josipovic said.
Milanovic had contended the referendum threatened people's right to happiness and choice.
Leaders of the opposition HDZ party supported the ban, which was supported by a petition drive that gathered 750,000 signatures.
The measure was drafted by the conservative organization In The Name of Family. It formally defines marriage as a heterosexual union.