Moderate cleric Hassan Rouhani has called his defeat of conservative hardliners a victory of moderation over extremism and pledged a new tone of respect in international affairs.
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
Thousands of jubilant Iranians poured onto the streets in celebration of the victory on Saturday, chanting: "Long live reform! Long live Rouhani!", according to witnesses at the scene.
"Ahmadi, bye bye!" they added in reference to President Mahmoud Ahmadinejad - who was legally barred from seeking a third consecutive term.
Many were dressed in purple, Rouhani's campaign colour, and others in
green, the colour of the reformist movement.
Rouhani will take up the presidency, the highest elected office in Iran's hybrid clerical-republican system, in August.
"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," Rouhani 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.
In his first televised address on Sunday Iran's president-elect asked for help during his term and promised to abide by Iranian law.
"[I'm proud that] the great people [of Iran], the honourable people, thought that I deserve this," Rouhani said.
"They trusted me so that I can begin on the path to serve the country, to enhance people's lives and welfare, and preserve national pride and national interests. I deeply feel that I need your assistance along this path. I need you to be there. I need your cooperation."
Rouhani won outright against five conservative candidates with 18.6 million votes, Interior Minister Mohammad Mostafa Najjar said.
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That was enough to ensure there would be no run-off against the runner-up, Tehran mayor Mohammad Baqer Qalibaf, who came a distant second with 6.07 million votes.
Saeed Jalili, Iran's Chief nuclear negotiator received four million votes and Mohsen Rezaei, a former head of the elite Revolutionary Guard, was also backed by close to 4 million people.
Matters of national security remain the domain of Iran's Supreme Leader Ayatollah Ali Khamenei, but the president runs the economy and wields broad influence in decision-making in other spheres.
Friday's vote was the first since the disputed 2009 re-election of Ahmadinejad triggered massive street protests by supporters of his rivals, that were crushed in a deadly crackdown.
The 2009 protests that followed Ahmadinejad's re-election led to the eventual house arrest of opposition candidates Mir Hossein Mousavi and Mehdi Karroubi, and the widespread suppression of reformists.
Al Jazeera's Soraya Lennie, reporting from Tehran, said that in the Iranian context, Rouhani is not exactly a true reformist but a moderate. She explained that moderates want to reform only the system but they want Iran to abide by its constitution and emphasise easing of restrictions on personal freedoms.
Rouhani, a former top nuclear negotiator who has championed more constructive engagement with world powers, seemed to strike a new tone in the way he talked about Iran's foreign relations in his statement.
He said there was a new chance "in the international arena" for "those who truly respect democracy and co-operation and free negotiation".
Though an establishment figure, Rouhani was known for his nuanced, conciliatory approach when he was Iran's chief nuclear negotiator.
He inherits an economy that has been badly hit by EU and US sanctions targeting the key oil and banking sectors because of its nuclear programme.
In 2003, when Rouhani was under former President Mohammad Khatami, the republic agreed to suspend its controversial enrichment of uranium.
That programme resumed two years later when Ahmadinejad was first elected.
In campaigning, Rouhani pledged to move to ease the sanctions, which have hit hard. Inflation is more than 30 percent, the rial has lost nearly 70 percent of its value and unemployment is rising.
Rouhani is a representative Khamenei on the Supreme National Security Council, Iran's top security body, and was its secretary for 16 years until 2005.
Emphasising political continuity, Khamenei congratulated both the people of Iran for the high turnout in the polls and Rouhani for his electoral success.
"The true winner of yesterday's election is the great nation of Iran that was able to take a firm step with God's help," Fars news agency quoted Khamenei as saying.
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As Iranians celebrate, the US, Israel, Russia and some Gulf countries have been giving their reaction to the election result.
Iran's rial strengthened about four percent against the US dollar on Saturday after partial vote tallies pointed to an easy Rouhani victory, web sites tracking the currency said.