The two sides, trying to build on an interim deal signed last week, agreed to a road map towards a permanent agreement within 60 days at the talks in the Swiss mountain resort of Burgenstock, mediators Pakistan and Qatar said.
They also agreed on a mechanism to end fighting in Lebanon between US ally Israel and Iran-aligned Hezbollah, and opened a communications line to help ensure safe passage for commercial ships through the strait, a vital global oil supply route.
Vance said Iran had agreed to allow in nuclear inspectors, and to establish mechanisms to handle its assets frozen abroad and manage ceasefires.
"We laid a very good foundation for a successful final deal," he told reporters after taking part in the talks.
Since the US bombed Iran's nuclear facilities in June last year, Iran has let the International Atomic Energy Agency inspect only facilities that were not attacked in those strikes.
The IAEA halted inspections altogether after the US-Israeli strikes that began the war with Iran on February 28 and they have not resumed since.
Vance played down tensions over a threat on Sunday by US President Donald Trump to restart the war after Iran again closed the Strait of Hormuz, citing a US failure to halt the fighting in Lebanon.
"There was a little bit of threatening, there was a little bit of whining, but at the end of the day the talks continued and we made great progress," Vance said.
Iranian Foreign Minister Abbas Araqchi said on social media that Iran had secured waivers for oil and petrochemical exports, the release of some of its frozen assets abroad and the launch of a reconstruction and development plan for Iran.
Vance said White House envoy Jared Kushner, Trump's son-in-law, had come up with a process where the US and Qatar would have control over Iranian funds when they are unfrozen that would allow the money to be spent on US corn, soy and wheat.
Following on from last week's interim deal, or memorandum of understanding, the US Treasury Department issued a general license for Iran on Monday authorising the production, delivery and sale of crude oil and petrochemical and petroleum products of Iranian-origin through August 21.
Technical talks were due to continue for the rest of this week, and Pakistani Prime Minister Shehbaz Sharif wrote on X that the first round of talks had "concluded successfully".
"The discussions were held in a positive and constructive atmosphere and yielded encouraging progress," he said.
