AFP journalists said crowds marched through Vali-Asr Square in central Tehran carrying pictures of the winner and chanting pro-Rowhani slogans.
In northwest Tehran, people gathered in Kaj Square and cheered as passing cars sounded their horns in approval.
Minister Mohammad Mostafa Najjar said Rowhani won outright with 18.6 million votes, or 50.68 per cent.
He said 36.7 million people - 72.7 per cent of the electorate - had voted on Friday out of an eligible 50.5 million.
The incumbent, Mahmud Ahmadinejad, had been constitutionally barred from standing again after serving two consecutive terms.
Najjar added that Tehran's conservative mayor, Mohammad Baqer Qalibaf, was runner-up with 6.07 million or 16.55 per cent of the votes.
Iran's top nuclear negotiator Saeed Jalili, who advocated resistance in Tehran's atomic talks with world powers, came third with 4.16 million (11.35 per cent).
Former Revolutionary Guards commander Mohsen Rezai and ex-foreign minister Ali Akbar Velayati won 3.88 and 2.26 million votes respectively.
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Congratulations.....we wish if elections in Pakistan last month had been as free and fair as yours.
I congratulate H.E. Hassan Rowhani on becoming President of Iran.
I hope that under his leadership the Pakistan-Iran gas pipeline project will be completed soon.