Without dissent, the high court reversed a state district judge's ruling in October striking down the amendment on the grounds that it violated a provision of the state constitution requiring that an amendment cover only one subject.
"Each provision of the amendment is germane to the single object of defense of marriage and constitutes an element of the plan advanced to achieve this object," the high court said.
The court's ruling puts the amendment in the constitution.
The amendment was sent to the ballot by the Legislature and approved by 78 percent of the voters on Sept. 18.
Legislative backers said that although same sex marriages are banned by state law, the amendment was needed to ensure that courts would not authorize the marriages, as had happened in Massachusetts.
In striking down the amendment, Judge William Morvant of Baton Rouge had ruled that the amendment also prevented the state from recognizing any legal status for common-law relationships, domestic partnerships and civil unions between both gay and heterosexual couples.