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A ministry spokesman says the moderate candidate received over 18 million votes, while his closest rival received just over 6 million votes.
The new president-elect received the backing of reformist leaders just before the vote, after speaking out against hardliners.
He was the only candidate to appeal to the large bloc of reform-minded voters while five more hardline contenders split the conservative vote.
His landslide win means there is no need for a run-off election.
After the election Mr Rowhani urged world powers to speak to his country with respect and acknowledge its rights.
“A new opportunity has been created by this great epic, and the nations who tout democracy and open dialogue should speak to the Iranian people with respect and recognise the rights of the Islamic Republic,” he said.
Then they will “hear an appropriate response,” he added.
Iran’s supreme leader Ayatollah Ali Khamenei congratulated Mr Rowhani on the win.
“Congratulations to the people and to president-elect Hojatoleslam Hassan Rowhani,” his website, leader.ir, reported.
“I urge everyone to help the president-elect and his colleagues in the government, as he is the president of the whole nation.”
Mr Rowhani was backed by the former reformist president Akbar Hashemi Rafsanjani, who was banned from running by the clerics in the so-called Guardian Council.
He campaigned on a promise to improve civil liberties and the economy and pursue a less confrontational relationship with the international community.
He says he wants to restore Iran’s ailing economy and fight discrimination against women.
While he has said there will be “no surrender” to the West on Iran’s controversial nuclear program, he has pledged to pursue a more constructive approach and hopes to ease sanctions.
The United States said on Saturday it is prepared to engage Iran “directly” over its disputed nuclear program after Mr Rowhani was elected.
The White House said such engagement would be aimed at reaching a “diplomatic solution that will fully address the international community’s concerns about Iran’s nuclear program”.
Mr Rowhani was the lead nuclear negotiator under the reformist president Mohammad Kathami and agreed to a freeze in Iran’s controversial uranium enrichment program in 2003.
He resigned shortly after Mahmoud Ahmdinejad was elected in 2005.
The moderate cleric says his victory marks a triumph over extremism.
Who is Hassan Rowhani?
Moderate cleric who has pledged to restore diplomatic ties with the US.
Has promised a more constructive approach to talks on Iran’s nuclear policy.
Has been an outspoken critic of outgoing president Mahmoud Ahmadinejad.
Served as a member of parliament from 1980 to 2000.
In 2000 became a member of the Assembly of Experts.
From 1989 to 2005, served as secretary of the supreme national security council, Iran’s top security post.
As nuclear negotiator from 2003 to 2005, oversaw a moratorium on uranium enrichment.
He has also pledged that “discrimination against women will not be tolerated” by his administration.
Born in 1948 in Sorkeh, he is married with four children.
He holds a doctorate in law from Scotland’s Glasgow Caledonian University.
