Vucic wants to negotiate Serbia's accession to the EU but keep close ties with the country's traditional ally, Moscow.
Putin told Vucic his victory "testifies to the wide support for your efforts aimed at resolving current economic and social problems ... and pursuing a constructive, balanced foreign policy," the Kremlin said in a statement Monday.
A hardline nationalist who became a pro-European, Vucic wants to negotiate Serbia's accession to the EU but keep close ties with the country's traditional ally, Moscow.
The 47-year-old, who will have a five-year term as president, won about 55 percent of the vote held Sunday, far above the 50-percent threshold required to win in the first round, according to the IPSOS research institute.
In Serbia the president's post is largely ceremonial but analysts say Vucic will use it to consolidate his grip on power, including with his eventual pick for prime minister.
The Kremlin said Putin had "expressed confidence that (Vucic's) work as head of state will promote the further development of the Russian-Serbian strategic partnership."
When asked by reporters whether Putin's support for Vucic had helped him win the election, Kremlin spokesman Dmitry Peskov replied: "Putin did not elect the president of Serbia. The Serbs elected their president. They were the ones who voted."
Putin hosted Vucic at the Kremlin last week, where they discussed bilateral relations.
Russia is a close ally of Serbia and does not recognise Kosovo's 2008 unilateral declaration independence, recognised by more than 100 countries.