After months of speculation, the "Mary Kom" actress took to her Instagram account to make it official that she is "taken" with her "heart and soul", while Jonas introduced her as the "Future Mrs Jonas".
Priyanka Chopra and Nick Jonas went to the Met Gala together last year but supposedly didn't date till this year.
Jonas apparently proposed on July 18 - Chopra's birthday - in London.
Friends and family members also took to Instagram to wish the happy couple.
"Wow. First I'm blessed with an incredible future brother-in-law, and now such a lovely, inside and out, future sister-in-law", Sophie Turner wrote in the caption. "Thank you all for your wishes and blessings".
Nick's older brother Joe Jonas also congratulated his brother on his engagement to the Bollywood starlet.More news: Dozens OD on synthetic marijuana in New Haven, Connecticut
Anusha Dandekar, who is a close friend to Priyanka, said the couple makes "love look so easy, handsome and special".
Earlier in the day, the couple kicked off their engagement celebrations with the traditional roka ceremony in Mumbai.
This is the first ceremony in Jonas's and Chopra's Indian wedding: becoming formally engaged before their families. Jonas wore a patterned shirt and dark trousers.
Chopra, who won the Miss World pageant in 2000, is one of Bollywood's most identifiable stars and one of the few to have achieved success in the West.
Priyanka Chopra, Alia Bhatt and Arpita Khan Sharma squeeze in the frame for Mushtaq Sheikh's selfie moment.
Chopra's cousin and close friend Parineeti Chopra also posted a photo from the night with the couple. Jonas' parents also wore Indian outfits.