But Israeli President Shimon Peres, who will be 90 in August, struck a more moderate tone, saying that Rowhani would shun the "extremist" policies of President Mahmoud Ahmadinejad.
Iran's pursuit of a suspected nuclear weapons programme is closely followed in Israel, where Netanyahu has described it as an "existential threat" to the existence of the Jewish state.
Israelis have been alarmed by Ahmadinejad querying Israel's right to exist and his denial of the Holocaust.
Professor Meir Litvak, the director of the Tel Aviv Centre for Iranian Studies, said he was surprised by the result, which sent a clear message from the Iranian population to the Supreme Leader that "Iranians don't want to starve because of his inflexibility on the nuclear issue".
Litvak said that under an "optimistic" scenario, Khamenei should be "more flexible" with the West in order to obtain some relief from sanctions which have brought economic hardship and a steep decline in the value of the Iranian currency.
But Litvak added that there was also a "pessimistic" scenario which would reflect the two faces of the Iranian regime, which is bitterly divided over how to engage with the West. Rowhani, described as a centrist with conservative tendencies, would be the "smiling face ... but the bad guys would keep doing what they are doing today".
As President, Rowhani has responsibility for the economy but otherwise his power is restricted. Litvak said there was a risk that he would disappoint the pro-reform supporters as the former reformist President Mohamed Khatami,had done in the past. Khatami and former President Akbar Hashemi Rafsanjani supported Rowhani. Rowhani, the only cleric in the running, was seen as the reformists' candidate in the closing days of the campaign.
But the Iranian President has no control over the judiciary, which is run by the hardliner Sadeq Larijani. It remains unclear whether the two leaders of the opposition Green Movement, Mir Hossein Moussavi and Mehdi Karroubi, will remain under house arrest, and whether Rowhani will be able to make good on his promise to seek the release of the hundreds of political prisoners jailed after Ahmadinejad's disputed victory in the 2009 election.
The Green Movement has been repressed after demonstrators took to the streets to contest what they saw as a rigged election in favour of Ahmadinejad, who is barred by the constitution from seeking a third term.
Public opinion in Israel remains opposed to the Israeli military taking unilateral action against Iran, despite Netanyahu warning that Israel would not tolerate the Iranians breaching a "red line" on uranium enrichment.
The Iranians had been careful to keep within Netanyahu's limit, said Gary Samore, President Barack Obama's former chief adviser on weapons of mass destruction, reached by telephone.
But Litvak said that Netanyahu had made a "major mistake" by singling out enrichment as the sole criterion that could prompt military action. Iran is also pursuing work on long-range missiles and a reactor for producing plutonium which could provide an alternative path towards a bomb should this be authorised by the Supreme Leader.
"That deprived Israel of an argument which means that the Iranians can't be judged on a broad front. If they decide to break the rules to go for nuclear weapons capability, they will be able to do it very quickly," said the Israeli academic.
Iran analysts said that the painful impact of sanctions might have contributed to the Iranian leader's decision to recognise Rowhani's victory. "They are staring in the face of the collapse of the economy which will threaten the regime," said Samore who is now at Harvard University's Kennedy School of government. But he added that unless Iran showed more flexibility, a further round of sanctions targeting the oil industry would be on the table. "It's an opening," said Samore. But will the Supreme Leader take it?
