The singer, whose real name is Tom Neuwirth, won with the song Rise Like a Phoenix, collecting 290 points.
The Netherlands finished second with 238 points, with Sweden in third place with 218 points.
The UK’s Molly Smitten-Downes came 17th, with 40 points for her song Children of the Universe.
It is the first time Austria has won the contest since 1966, and only the second time the country has competed in the final in the past 10 years as it either did not participate or qualify.
Wurst had been the second favourite to win behind Sweden going in to the competition, with many predicting the act could be too divisive among voters.
However she was the clear winner, with her victory announced after 34 of the 37 countries had submitted their scores.
Collecting her trophy on stage the singer said: “This night is dedicated to everyone who believes in a future of peace and freedom. You know who you are – we are unity and we are unstoppable.”
“I dream of a world where we don’t have to talk about unnecessary things like sexuality, who you love. I felt like tonight Europe showed that we are a community of respect and tolerance,” she said.