The president first issued the directive to kill Soleimani in June, after Iran shot down a US drone, the report said.
The order authorised the assassination in response to any Iranian attacks resulted in the death of American citizens, the report said, adding that Trump's directive came with the condition that he would have the final authority to sign off on the operation.
Trump gave his final approval for the assassination after the storming of the embassy in Baghdad on 31 December, according to the report.
The reported timing of the presidential order appears to undermine Trump's assertion that he authorised the assassination after learning that Soleimani was planning "imminent" attacks on US embassies in the Middle East.
The United States killed Soleimani and Iraqi Shiite militia leader Abu Mahdi Muhandis in an operation on 3 January near the Baghdad International airport.
Just a week before the assassination, the United States blamed the Iranian-backed Kataib Hezbollah militia for an attack on a US military base near the Iraqi city of Kirkuk that killed a US contractor on 27 December. The US retaliated by striking Kataib Hezbollah's forces in Iraq and Syria, killing about two dozen of its fighters.
That retaliatory operation, in turn, triggered protests at the US Embassy in Baghdad on 31 December during which demonstrators stormed the facility and set fire to its outer perimeter. The United States then blamed Soleimani for orchestrating the protests at the embassy.