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.