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.