* Rohani calls his win triumph over "extremism"
* Calls for a new tone in Iran's foreign relations
* Jubilant crowds celebrate win in Iran's major cities
Moderate cleric Hassan Rohani won Iran's presidential election on Saturday with a resounding defeat of conservative hardliners, calling it a victory of moderation over extremism and pledging a new tone of respect in international affairs.
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 programme 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.
"LONG LIVE REFORM!"
"Long live reform! Long live Rohani!" chanted the throngs, according to witnesses at the scene. "Ahmadi, bye bye!" they added in reference to Ahmadinejad, the witnesses said.
"Tehran has exploded with happiness. I have never seen so many people so happy in my life," said Negin, a 29-year-old photographer.
Others flashed the victory sign and chanted slogans in favour of Mirhossein Mousavi, who reformist supporters believe was robbed of the 2009 election by what they say was vote rigging to return Ahmadinejad to office.
"Mousavi, Mousavi, I got back your vote!" and "Mousavi, Mousavi, congratulations on your victory!" the crowds shouted.
Another eyewitness named Mina told Reuters tearfully by phone: "I haven't been this happy in four years. I feel that we finally managed to achieve a part of what we have been fighting for since the past elections. They finally respected our vote. This is a victory for reforms and all of us as reformists."
Rohani will take up the presidency, the highest elected office in Iran's hybrid clerical-republican system, in August.
Several people were killed and hundreds detained when security forces crushed protests after the 2009 election, and Mousavi and his fellow reformist candidate are still being held under house arrest. Authorities say the election was free and fair.
Though an establishment figure, Rohani was known for his nuanced, conciliatory approach when he was Iran's chief nuclear negotiator.
He could act as a bridge-builder between hardliners around Khamenei who reject any accommodation with the West and reformers marginalised for the last four years who argue that the Islamic Republic needs to be more pragmatic in its relations with the world and modernise at home in order to survive.
Emphasising political continuity, Khamenei congratulated both the people of Iran for the high turnout in the polls and Rohani 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.
But Rohani's wide margin of victory revealed a large reservoir of support for reform with many voters, undaunted by restrictions on candidate choice and campaign rallies, seizing the chance to rebuke the unelected elite over Iran's economic miseries, international isolation and security crackdowns.
Rohani's nearest rival was conservative Tehran Mayor Mohammad Baqer Qalibaf, a long way behind with less than 16 percent. Other hardline candidates close to Khamenei, including current nuclear negotiator Saeed Jalili, scored even lower.
Iran's rial strengthened about 4 percent against the U.S. dollar on Saturday after partial vote tallies pointed to an easy Rohani victory, web sites tracking the currency said.
Washington said it stood ready to engage with Iran to reach a "diplomatic solution" over its nuclear programme, which the West suspects is intended to produce nuclear weapons - something Iran denies.
"We respect the vote of the Iranian people and congratulate them for their participation in the political process, and their courage in making their voices heard," the White House said in a statement.
"It is our hope that the Iranian government will heed the will of the Iranian people and make responsible choices that create a better future for all Iranians."