The students had secured 52.65% of the vote, while Vučić's Serbian Progressive Party (SNS) was on 39.2%, according to its preliminary figures released late on Monday morning. Earlier in the day, long queues were seen outside polling stations in cities and towns across Serbia.
The student movement was formed less than two years ago in response to a railway station disaster blamed on corruption and negligence, but fought the election with candidates from a cross-section of Serbian society. The anti-corruption movement campaigned on a manifesto that included purging officials who broke rules cracking down on protesters, stopping party loyalists from leading public enterprises, and freeing the public broadcaster of political control.
Celebrations erupted as crowds descended on the centre of Belgrade, Novi Sad and other cities. There were celebrations on the streets of the city, with people dancing and chanting"victory", cars honking, and fireworks set off.
The stunning shift marks a major political turning point for the country, ending years of dominance by Vučić and his ruling party following an election triggered by widespread public anger.
Serbia's long-standing leader Aleksandar Vučić has admitted defeat to a student-led protest movement in snap parliamentary elections.
The centre of Novi Sad - the northern city that triggered the student-led protests - was crowded.
Vučić made his announcement at the headquarters of his Serbian Progressive Party (SNS) in the capital Belgrade.