Vucic's resignation on Sunday, seven months before his term ends, comes amid campaigning for Serbia's October 25 snap parliamentary vote and allows him to be appointed prime minister if his Serbian Progressive Party (SNS) forms the new government.
Hundreds of Vucic's supporters cheered him in front of the Presidency building in Belgrade's city centre.
"This is the last evening for me in this building," he told the flag-waving crowd minutes before resigning.
"I have faithfully served you and my fatherland, Serbia, ... I am proud of what we have done together," he said.
Under Serbia's constitution, outgoing parliament Speaker Ana Brnabic will serve as interim president until a new one is elected. The presidential election must be completed within 90 days, with the campaign lasting between 30 and 60 days.
"By the end of December ... we will have the first round of presidential elections," said Vucic, who had announced his intention to resign as president earlier in the summer.
The snap parliamentary election next month pits Vucic's SNS and its allies against Students Win, a student-led anti-corruption movement, and European Serbia, an alliance of pro-Western opposition parties.
Students Win, European Serbia and other parties still have to nominate their presidential candidates.
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