Vucic, 47, will have a five-year term as president.
Mr Vucic has been prime minister since 2014.
However Vucic claims to be a pro-Western politician seeking to join the European Union while at the same time keeping close relations with traditional ally Russian Federation to please his mainly Serbian Orthodox voters.
"I am very proud of the fact we received a huge number of votes in conditions that were anything but easy for us, this is an important day for us and it's important to show the direction Serbia wants to go".
"For me it is important this election demonstrated that a large majority of Serbian citizens favours the continuation of the European parh while maintaining close ties with China and Russian Federation", he told cheering supporters.
Peskov said it was the Serbian people and not Vladimir Putin who elected the new Serbian president and so it is inappropriate to make allegations on whether Putin's support for Vucic could have influenced the voters.
Cupic said it was unsafe and bad for democracy to host a prime minister who was competing for the presidency.
Hahn told reporters that he was comforted by Vucic's early assurances that "he will fully respect the constitutional framework, and I trust him".
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"Mr Vucic will be moving into the presidential palace in two months".
Vucic, a conservative who had been serving as Serbia's prime minister, claimed 55 percent of the vote, avoiding a runoff and soundly defeating the leading opposition candidate, Sasa Jankovic. Despite economic growth and greater fiscal stability, Serbia remains mired in poverty and corruption.
Vucic had also run a typically aggressive campaign, with one of his videos showing a plane marked "Serbia 2017" about to crash because a lack of leadership.
He has accused opponents of receiving "millions of euros (from) certain foreign countries", without offering specifying charges. Running as an independent, Jeremic is supported by right-leaning opposition groups.
That rose to 67 percent when his appearances as prime minister were taken into account, added the analysis.
"I was convinced that the SNS candidate must win in the first round and that a second round would effectively mean failure", Nikolic, whose presidential mandate expires on May 31, said.
Jankovic is the closest rival to Vucic with an estimated 12 percent support.
Vucic was named as the front-runner before the voting. He easily eclipsed second-place challenger Sasa Jankovic, a former ombudsman, who won 14.89 per cent. Vucic declared himself the victor after parallel counts from polling agencies showed him with a majority.


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