Photos posted on the Iranian Mehr News website showed young Iranians celebrating in the streets after it was announced that Rouhani won more than 50 percent of the votes in Friday's 11th presidential elections.
"I will remain loyal to the promise that I made with the Iranian nation," he said in his first televised speech, the Iranian Students News Agency said.
Iran's Supreme Leader Ayatollah Ali Khamenei congratulated Rouhani on the election outcome, Press TV said.
"The real winner of yesterday's election is the great Iranian nation which ... prudently and tactfully confronted the war of nerves launched by the lackeys of hegemony," Khamenei was quoted as saying.
Rouhani won a total of 52.4 percent of the votes constituting 18.6 million out of a total of 36.75 million ballots counted, the semi-official Fars News Agency said Sunday. Mohammed Baqer Qalibat, the mayor of Tehran, came in a distant second with 6.07 million votes, the agency said. Iran's Interior Ministry said there was a 72.7 percent turnout, Fars said.