The agreement on Monday would extend a tenuous ceasefire announced in April by another 60 days and reopen the Strait of Hormuz, which Iran has effectively blocked since the US and Israel attacked Iran in February.
Negotiators would address difficult issues like the future of Iran's nuclear program during the next phase.
"The deal's all signed," Trump said after he arrived in France for a summit of the G7 group of big economies.
He said Vice President JD Vance would attend a formal signing ceremony in Geneva on Friday.
Oil prices fell to their lowest level since March 10, shortly after the blockade of the Strait of Hormuz, a narrow waterway between Iran and Oman, cut off one-fifth of the world's oil trade.
The deal is the most significant step yet to resolve the conflict, which has killed at least 7000 people, mostly in Iran and Lebanon, and upended global energy markets. But much about the agreement remains unknown, and whether its provisions differ from the April ceasefire was unclear.
Iranian President Masoud Pezeshkian wrote on social media the US-Iran memorandum of understanding was an "important step" toward stopping the fighting but noted a final agreement for a lasting truce "has yet to take shape".
US officials, speaking on condition of anonymity, said Iran would have to satisfy US demands never to build a nuclear weapon and cut off support for militias like Hezbollah in Lebanon in order to get those benefits.
Iran agreed to sharply curtail its nuclear program in a deal signed in 2015 with the US and other countries. Trump withdrew the US from that accord during his first term as president. That agreement allowed Iran to regain billions of dollars in frozen assets, which Trump has frequently derided as sending "pallets of cash" to Iran.
Trump appears to have achieved little of what he said he intended when he launched strikes on Iran with Israel on February 28. Iran's theocratic government remains in place, while his demands that Iran dismantle its ballistic missile program and end support for regional militias like Hezbollah remain unmet.
The new agreement also does not resolve the fate of Iran's stockpile of enriched uranium, which Trump says he wants destroyed or removed.
Iranian officials, who have always denied intending to build a nuclear weapon, say they have given up little by agreeing to resume the diplomatic discussions with Trump officials over the nuclear program that were interrupted in February by Trump's decision to launch the war.
While the latest agreement lifts Iran's chokehold on the Strait of Hormuz, that only restores the prewar status quo, and shippers say traffic will only restart once safety is assured.
Iran has suggested it will retain control with Oman over the strait. The US said the strait will be open toll-free for 60 days and it would expect that provision to be part of a final agreement as well.
The fighting between US ally Israel and the Iran-allied Hezbollah militia in Lebanon, which has uprooted 1.2 million people, remains a sticking point.
A US official said Israeli withdrawal from Lebanon, which it invaded in March after Hezbollah joined the war, was not a condition of the deal. Disagreement over whether Lebanon was included was also a point of contention in the April ceasefire agreement.
Iranian Foreign Minister Abbas Araqchi said Israeli attacks must stop immediately. Privately, Israeli officials' views of the deal have been negative. One senior official told Reuters on condition of anonymity that the agreement was "terrible for Israel," and that this assessment was shared throughout the government from Netanyahu down.
with PA
