Australians were encouraged to vote via text message for their favourite performer.
It was the second time since Australia joined the Eurovision Song Contest in 2015 the country's performer was chosen via a public vote.
The public was responsible for 50 per cent of the decision, with the other half falling to a panel of industry professionals.
Following the announcement of her win, Montaigne said she was “ecstatic, euphoric [and] energetic."
“It’s really exciting for me. I was quite nervous because I was nervous about being nervous, because that might affect my signing while I do something different," she said.
“I don’t know if I sung the song perfectly, but I think I did a pretty good job.”
Jon Ola Sand, Eurovision Executive Supervisor, said Montaigne put on a "very creative, different performance".
“An act always develops for Eurovision, but her act as it is now, is really strong," he said.
Peter Verheij, the Australian delegation host, said Montaigne would be "very much welcomed in the Netherlands.”
“I think [Europe will] love it – it’s different, very nice act,” he said.
Among the other contestants was Gamilaraay singer Mitch Tambo, who garnered attention with his 26 January performance of John Farnham’s You’re The Voice, which he performed in his traditional language.
Tambo said the competition was a chance to show the world that Indigenous Australia culture was alive and thriving.
“No matter where we come from, no matter what gender we are, sexuality, culture, religion, race … we just need to come together and love one another,” he said.
Had he been successful, Tambo would have been the third Indigenous Australian to grace the Eurovision stage in Australia’s five years as part of the contest, after Isaiah Firebrace performed in 2017 and Jessica Mauboy in 2018.
The other contestants vying for the opportunity to represent Australia were veteran performer Vanessa Amorosi, Australian Idol winner Casey Donovan, The Voice winner Diana Rouvas, singer-songwriter Jordan-Ravi, emerging artist Jaguar Jonze, rock performer iOTA, alternative artist Didirri, and Jack Vidgen, who first came to public attention when he won Australia’s Got Talent at 14 years of age.
Inaugural Eurovision – Australia Decides winner Kate Miller-Heidke, Sweden's 2015 Eurovision winner Måns Zelmerlöw, and last year's Junior Eurovision representative Jordan Anthony took to the stage alongside contestants on Saturday night.
Korean-born singer-songwriter Dami Im, who came second at Eurovision 2016 with her song Sound of Silence, also performed.
Fans went into overdrive when she announced on Saturday night that she was intending on 'throwing her hat in the ring' for 2021.
The 2020 Eurovision Song Contest takes place 12- 16 May in Rotterdam, Netherlands.
Additional reporting by Maani Truu, Charlotte Lam and Evan Young