Though thousands of jubilant Iranians poured onto the streets in celebration of the victory, the outcome will not soon transform Iran's tense relations with the West, resolve the row over its nuclear program or lessen its support of Syria's president in the civil war there - matters of national security that remain the domain of Supreme Leader Ayatollah Ali Khamenei.
But the president runs the economy and wields broad influence in decision-making in other spheres. Rohani's resounding mandate could provide latitude for a diplomatic thaw with the West and more social freedoms at home after eight years of belligerence and repression under President Mahmoud Ahmadinejad, who was legally barred from seeking a third consecutive term.
"This victory is a victory of wisdom, a victory of moderation, a victory of growth and awareness and a victory of commitment over extremism and ill-temper," Rohani told state television, promising to work for all Iranians, including the hardline so-called "Principlists" whom he defeated at the poll.
"I warmly shake the hands of all moderates, reformists and Principlists," he said.
The mid-ranking cleric seemed to strike a new tone in the way he talked about Iran's relations with the rest of the world.
Rohani said there was a new chance "in the international arena" for "those who truly respect democracy and cooperation and free negotiation".
Celebrating crowds sprang up near Rohani's headquarters in downtown Tehran and across the city and country as his victory was confirmed.