An exit poll indicated the ban was adopted by about a 3-to-1 margin. Same-sex marriages are already illegal in Georgia, but the matter had not been addressed in the state constitution.
One of the ban's biggest supporters, Sadie Fields of the Georgia Christian Coalition, cheered its approval by voters.
"I've said all along that this crossed party lines, color lines and socio-economic lines. It went beyond all that," Fields said. "The people in this state realized that we're talking about the future of our country here, what we want the future to look like for our children."
The ban's passage was based on a statistical analysis of the vote from voter interviews conducted for The Associated Press by Edison Media Research and Mitofsky International. It tracked a pre-election poll.
The exit poll showed that men and women backed the ban in similar numbers, as did every wage bracket and age group. Both Democrats and Republicans supported the ban. More than three quarters of blacks supported it -- slightly higher than its support among white voters.
Nor was the support limited to voters who referred to themselves as voters as white evangelicals or born-again Christians. Although nearly nine of 10 of them voted for it, almost two-thirds of others did as well. Even four of 10 voters who said they never attend church services backed the amendment.
Some voters said they support some gay rights -- just not marriage.
"If gays want to get married, they should call it civil union -- not marriage," said Tudi Southerlin, 48, a Gwinnett County Republican. "I used to think it was disgusting, but God has made people all different ways, and everyone has the right to choose their own partner."
Gay rights supporters have vowed to go to court over the amendment, saying it was illegal because it contained more than one subject. They said the amendment could apply not just to same-sex marriages, but to other rights.
"We will not give up. We will not give in," said state Rep. Karla Drenner, a Democrat and leader of Georgians Against Discrimination, which worked to defeat the amendment.
"We will continue to tell the truth about our lives. We will not go quietly into anyone's dark and silent night."
Gay-rights supporters already have filed one lawsuit against the amendment, which tried to pull it from the ballot. The state Supreme Court refused to block the ballot measure, saying the judicial branch couldn't interfere until after the process of adopting an amendment was over. That lawsuit is expected to be revived now that the vote is over.