Megan Young beat five other finalists, including France and Brazil, to win the coveted title in a contest broadcast to more than 180 countries worldwide.
She thanked the judges for choosing her and promised to "be the best Miss World ever".
The 23-year-old pledged to "just be myself in everything I do, to share what I know and to educate people".
The decision to hold the pageant in the world's most populous Muslim-majority country had sparked hardline anger. Heavily armed police and water cannon were guarding the venue in Nusa Dua, southern Bali.
Thousands of hardliners had taken to the streets around the country to protest against the pageant in recent weeks, and radical group the Islamic Defenders' Front had pledged to stage protests on Saturday against the pageant.
But in the end no demonstrations materialised, and the group limited itself to holding a mass prayer session in a mosque just outside the capital Jakarta to express their opposition.