Mans Zelmerlow won with his upbeat pop track Heroes, which was accompanied by innovative animated visuals.
Italy came on the third place, followed by Belgium. Australia finished fifth in the country’s first Eurovision appearance.
A record number of countries – 27 – took part, including Australia – which was invited to compete for the first time to mark the event’s 60th anniversary.
Mans Zelmerlow was the bookmakers’ favorite throughout the build-up to this year’s contest.
“I’m so happy and I want to say thank you for voting for me,” he told the crowd.
“I want to say we are all Heroes, no matter who we love, who we are or what we believe in – we are all heroes.”
This is Sweden’s sixth Eurovision win – meaning they are now just one victory behind the contest’s record holders Ireland, who have won seven times.
The result also means the next year’s song contest will be held in Sweden – just three years after it last hosted the show.
This year’s contest was held in the Austrian capital’s Wiener Stadthalle following Conchita Wurst’s win last year.
But this year, the hosts, along with Germany, finished with zero points – the first time since 2003 that any country has drawn a blank.
Russian contestant Polina Gagarina was beaten by Mans Zelmerlow after being neck-and-neck for much of the voting.
Italian opera trio Il Volo who have enjoyed chart success around the world, finished third. Belgium’s 19-year-old Loic Nottet managed fourth.
And it was a respectable night for Guy Sebastian, one of Australia’s biggest pop stars, who came fifth after being sent to represent his country.
After the show, Eurovision organizers revealed there had been irregularities with the votes from the juries in Macedonia and Montenegro.
The points awarded by each country are normally determined by a combination of a jury and a public vote.
A statement said: “The jury results of FYR Macedonia and Montenegro for the grand final have been excluded after consultation of PricewaterhouseCoopers, the contest’s independent voting observer, and upon the decision of the executive supervisor and the chairman of the reference group.
“In both countries, televoting applied for 100%. The exclusion of two juries will be further discussed in the next reference group meeting in June.”
Around 200 million viewers were thought to have tuned in to the event on television, and it was screened live in China for the first time.
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