The couple are celebrating their nuptials with friends and family at the lavish Umaid Bhavan Palace in the Rajasthani city of Jodhpur.
Jonas and Chopra got engaged in the summer after a whirlwind romance.
On social media, they said their wedding was an "amalgamation" of their families, faiths and culture.
They shared pictures of the traditional mehendi ceremony, in which Chopra had her hands and feet decorated with henna by the women of both families. There was also a cricket match between Team Priyanka and Team Nick ahead of the wedding.
People magazine said Saturday's Christian ceremony was officiated by Jonas's father Paul Kevin Jonas, a pastor. Both the bride and groom wore Ralph Lauren outfits, the designer tweeted.
There ceremony was followed by fireworks.
Jonas, 26, and Chopra, 36, got engaged in the summer, not long after news of their romance became public.
They have since said in an interview that they first started exchanging texts in September 2016. They appeared together at the Met Gala in May 2017 as they had both been dressed by Ralph Lauren, and their relationship started making headlines around a year later.
Chopra is one of Bollywood's highest-paid actresses, having won the Miss World pageant in 2000 and going on to make more than 50 films in India.
She broke in to acting in the US with a part in the TV series Quantico and film roles in Ventilator, Baywatch and A Kid like Jake.