The Russian-born model from Toronto was chosen out of five finalists - the four others from Latin America - who answered random questions onstage in the final round of the 54th annual pagent.
The 12-judge panel chose beauties from Mexico, Puerto Rico, the Dominican Republic, Venezuela and Canada as finalists.
Glebova, 23, was picked over runner-up Cynthia Olavarria of Puerto Rico after answering a final question about what she considered her biggest challenge in life.
"I'm the kind of person who looks at the glass half full," she said, adding that remaining optimistic was most challenging. "I always try to maintain a positive outlook on life."
Glebova - who emigrated from Russia to Canada with her family 11 years ago - posed for photos after the ceremony in a long white dress, standing with Thai Prime Minister Thaksin Shinawatra and other local officials. Her parents stood by with Canadian diplomats.
"I feel like this is happening too fast and it's unreal," Glebova told reporters. "It's just starting to sink in. I'm so much looking forward to the year's schedule."
She said she planned to use her role as Miss Universe to raise awareness and money for HIV/AIDS research.
Last year's title winner, Jennifer Hawkins of Australia, described her achievement as a fairy tale-like experience. But she said her later work publicizing humanitarian projects underscored the real-world responsibilities that come with the crown.
Thailand hoped the pageant would boost its tourism sector, which was badly hurt by last December's tsunami. It estimated that the event and related activities would generate more than 2.1 billion baht (US$54.6 million) of revenue.
"I hope that the Miss Universe contest will help encourage tourists back to the tsunami-hit areas," said Vijit Naranong, president of the Thai Tourist Association's southern chapter.
Pageant contestants arrived in Thailand about three weeks ago and have since visited tsunami-struck areas along the southern coast and historic Buddhist temples around Bangkok.
Photos of bikini-clad contestants posing near a revered temple stirred up a controversy in the predominantly Buddhist country. The images showed the contestants aboard a boat on the Chao Phraya river with Wat Arun, the famous Temple of the Dawn, in the background.
After the Thai government complained about the images two weeks ago, organizers pulled them from the pageant's Web site and video footage for Tuesday's competition.
The contestants also have driven the country's famous three-wheeled motorcycle taxis, called tuk-tuks, and ridden atop elephants - Thailand's national symbols.
By Daniel Lovering