US-born Megan Young, a 23-year-old studying digital film, accepted the crown from last year's winner, Wenxia Yu of China, and promised to "be the best Miss World ever".
Thousands of members of the radical Islam Defenders Front took to the streets over the past month to protest holding the pageant in Indonesia, the world's most populous Muslim country, calling it "pornography".
The protests forced organizers to move the event from a venue outside Jakarta to Nusa Dua in southern Bali, a predominantly Hindu resort island.
Event organizers announced in June that contestants would eschew bikinis this year in favour of sarongs and one-piece swimwear to avoid causing offence.
The embassies of the United States, Britain and Australia issued travel warnings for Indonesia, saying extremist groups could be planning violence to disrupt the pageant.
However, Indonesian police said there were no reports of unrest surrounding the contest on Saturday.
The new Miss World will spend the next year travelling to represent the Miss World Organization and help raise money for its charitable causes.
Marine Lorphelin, a 20-year-old medical student from France, took second place. From Ghana, Carranzar Naa Okailey Shooter, 23, also a medical student, came third.