Vucic, a populist and nationalist, has dominated Serbian politics as prime minister or president since 2014.
But he called snap elections in September after almost two years of student-led demonstrations against perceived corruption and creeping authoritarianism triggered by the deaths of 16 people when a train station canopy collapsed in the city of Novi Sad in 2024.
"It is clear that we have lost these elections, the Student List has won," Vucic said in a televised speech on Sunday.
Within moments of his announcement, the streets of Belgrade erupted in celebration. Tens of thousands of people thronged along the city's main boulevards, with cars honking, people dancing and students shouting "victory" and "he's done".
The students' win marks a profound political shift in the country of some six million people and is reminiscent of the defeat of Hungary's Viktor Orban in April.
It may also offer a blueprint for other student movements across Europe, which have taken to the streets in recent weeks to protest, in some cases violently, against poor education standards and a lack of prospects.
Vucic said the students would have between 135 and 140 seats in the 250-seat parliament and that his Serbian Progressive Party would have 105, based on preliminary results.
"Dear Serbia, tonight the voice of the people is being heard," said Radomir Sajcic, a professor at Belgrade University, speaking on behalf of the students at their headquarters.
"Tonight we celebrate victory, tomorrow we build the future."
European leaders and officials congratulated the Student List on its victory, among them President of the European Commission Ursula von der Leyen and European Commissioner for Enlargement Marta Kos.
"We stand ready to ... work together to advance Serbia's future in the European Union," von der Leyen wrote on X.
Hungarian Prime Minister Peter Magyar assured the students of his country's support.
Lines snaked from polling stations in cities and towns across the country earlier in the day, and even Vucic waited for nearly two hours to vote in Belgrade.
Pollsters and the election commission put turnout close to 70 per cent, the highest since the breakup of Yugoslavia in 1992.
Vucic, who resigned from his second term as president to run again for prime minister, was a strong incumbent and few in the student protest movement dared believe he would concede so fast.
Much remains unclear about how the student-backed candidates will fare.
Their list of 250 largely unknown candidates includes university professors, actors and farmers, and is led by cardiologist Ilija Srdanovic, who was in tears after Vucic's announcement.
However, it is unclear who will be prime minister and enact the students' domestic agenda, which aims to root out graft and improve schooling.
Political analysts predict some kind of purge of Vucic allies in the police, security services and ministries.
The student-led street protests sparked by the station disaster started small but quickly became the biggest in a generation, calling for Vucic to step down.
Vucic and the SNS repeatedly denied accusations of repression, corruption and spying on their opponents. He has said the students are funded by foreign agents in Croatia and Montenegro, a charge the students dismiss.
with AP
