A Christian minister and longtime friend of Perry's family performed a "private and spiritual ceremony," which was attended by family members and close friends, said the statement released by the couple's representatives.
"The backdrop was the inspirational and majestic countryside of Northern India," said the statement, which did not provide any further details on the ceremony.
The wedding was held at the Aman-e-Khas luxury resort in a tiger reserve in Ranthambhore National Park, a hotel official said on condition of anonymity as he was not authorized to speak to the media.
Security has been stringent with private security guards stationed at the resort and other nearby hotels where guests and the couple are staying for the six-day wedding celebration.
Photographers and media reporters were not allowed into the Aman-e-Khas wildlife retreat. The couple have given the exclusive coverage rights to a London magazine, and no other photographers or journalists will be allowed into the resort.
The wedding venue was lit with lamps, colorful lights illuminated the trees and flower garlands festooned the luxury tents at the resort, the hotel official said.
Both Brand and Perry wore traditional Indian clothes to the wedding, the hotel official said. Perry donned a sari, as did a number of other female guests at the ceremony. On Friday, at a prenuptial celebration, Perry, like a typical Indian bride, had henna designs applied on her palms and hands.
Meanwhile, a four-member committee had been set up to check noise pollution from the wedding celebration and ensure that animals in the wildlife reserve in India's Rajasthan state are not disturbed, said Ravi Kumar, a district official.
Ranthambhore National Park is home to a host of wildlife species including tigers, leopards, wild boars, hyenas and sloth bears.
The British comedian's wedding procession, accompanied by traditional Indian musicians, made its way from Sher Bagh, another nearby luxury resort, to the Aman-e-Khas retreat.
Brand proposed to the American pop singer, whose parents are Christian pastors, in the historic Indian city of Jaipur over New Year's Eve, and the couple decided to get married in India.
The 26-year-old Perry's single "California Gurls," from her second album "Teenage Dream," was one of the top hits of the year.
Brand, 35, is known for his drug-addled past and hedonistic tendencies, but says he has lived a sober life for the last few years. He recently starred in the hit film comedy "Get Him to the Greek," and is next set to star as Trinculo in Shakespeare's "The Tempest" and as the title character in a remake of the 1981 Dudley Moore-Liza Minnelli film "Arthur."
