Perry, 26, married 35-year-old Brand in front of about 80 guests at the luxury Aman-I-Khas resort near the animal sanctuary, UsMagazine.com reported.
Prior to Saturday's ceremony, Perry was spotted wearing traditional Indian clothing and a bridal nose ring, which is removed by the groom on the wedding night, the report said.
"We just love each other and we want to get married in front of our friends and family and keep it very normal," Brand said earlier in a New York Times report. "It ain't about selling the pictures, it ain't about doing no pre-nup, it's just a normal thing."
The magazine said Brand planned to ride into the ceremony on a horse, flanked by camels and elephants, while Katy planned to have a rotating designer bridal wardrobe, including a gown by Elie Saab.
"I think people get the wrong idea on how we want the wedding to play out. Love between two people is the most spectacular, yet ordinary thing in the world," Brand said.
He and Perry met in December near where the ceremony took place, the report said.