State TV offered its congratulations in a brief statement on Saturday.
With almost all votes counted from the previous day's election, Rouhani had an insurmountable lead with 58.6 percent of the vote, compared with 39.8 percent for his main challenger hardliner Ebrahim Raisi.
"I am very happy for Rouhani's win. We won. We did not yield to pressure. We showed them that we still exist," said 37-year-old Mahnaz, a reformist voter told Reuters. "I want Rouhani to carry out his promises."
Deputy Interior Minister Ali Asghar Ahmadi told journalists in a televised news conference earlier in the day that more than 40 million Iranians voted in Friday's election. That puts turnout above 70 percent.
In 2013, Rouhani won the presidential election with nearly 51 percent of the vote. Turnout for that vote was 73 percent.
Iran's president is the second-most powerful figure within Iran's political system. He is subordinate to the supreme leader, who is chosen by a clerical panel and has the ultimate say over all matters of state.
Friday's vote was largely a referendum on Rouhani's more moderate political policies, which paved the way for the landmark 2015 nuclear deal that won Iran relief from some sanctions in exchange for curbs on its nuclear program.
Rouhani has come to embody more liberal and reform-minded Iranians' hopes for greater freedoms and openness at home, and better relations with the outside world.
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