The feeling soon turned into joyful scenes in Tehran, with people dancing on the streets in the early hours of Friday as car horns blared and Iranians spoke of their hopes for a different future.
"Whatever the final result of the negotiations, we are winners," said Behrang Alavi, a 30-year-old actor, on Val-e-Asr Avenue at around 1:00 am as the noise reverberated around him on the capital's longest street.
"Now we will be able to live normally like the rest of the world," he added, as people flashed V-signs for victory and waved white handkerchiefs in the air in a traditional Iranian celebration.
It was Foreign Minister Mohammad Javad Zarif who had signalled a breakthrough was at hand after eight days of around-the-clock nuclear talks in Switzerland.
"Found solutions. Ready to start drafting immediately," Zarif wrote in his first post in five days on Twitter, which despite officially being banned is accessed by millions of Iranians using illegal software.
Minutes later pictures and his words in Farsi flowed into living rooms in the capital, announcing live that there was now a framework to end a 12-year crisis that has seen sanctions ravage Iran's economy and bring hardship to millions.
A June 30 agreement that would lift the sanctions in exchange for curbs and stringent international monitoring designed to ensure Iran cannot develop an atomic bomb is now tantalisingly within reach.
- Selfies with Obama -
Fatemeh Hashemian, 26, said she wanted a nuclear deal to help foreigners see her country in a better light.
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"I wish Iran could make progress like this everyday and have no more sanctions imposed on the country," she said.
"I hope that this wrong image of Iran will be erased. And that our relations with the world can improve."
In a sign of the mooted agreement's potentially enormous historical impact, Iranian state television screened US President Barack Obama's televised address live, with translation in Farsi.
As Obama was speaking, young Iranians took selfies with the president in the background and posted the pictures on Twitter.
But although there was hope, some Iranians said they wouldn't be convinced that anything would change until a deal is signed and sealed.
"It's not clear until we can see it in action," said Reza Riahizadeh, a 39-year-old engineer who was watching at home on television with his family.
"They might dodge cancelling the sanctions. No one knows. Nothing is certain until it is done in reality."
But Hassan Khudiarah, a 38-year-old taxi driver waiting for a fare halfway through a shift that would not end until 7.00 am, was more optimistic.
"It is a very good step for us," he said as fellow drivers stepped out of their cars to share the news at Argentine Square in downtown Tehran.
"I hope one day our problems will end and we will be treated as a friend by those who don't seem to like us, but don't know us. We don't want conflict."