Prosecutors said Rafat Amirov and Polad Omarov were to be paid $500,000 by Iran for the assassination.
Trump has also promised to release documents on the assassinations of civil rights leader Martin Luther King Jr. and Senator Robert Kennedy, both of whom were killed in 1968.
Such assassinations and commando operations could lead to escalation and a gradual heating up of the situation, said sources.
The attack involved a decade of intelligence collected both by the IDF and the Mossad, as well as a variety of last-minute deceptions.
"Everything will be revealed," Trump said as he signed the order, then holding it up.
The EU must take decisive action to counter the growing threat posed by Iran and the IRGC.
Two days after the murder, Iran still doesn't know the motive of the assassinations, sparking rumors of civil unrest.
Piersanti Mattarella was assassinated in front of his home in Palermo while in a car with his wife as they were heading to Epiphany Day Mass.
The figure urged Israel to target one of the Houthi's key military commanders, Abdullah Yahya al-Hakim, who he described as the "military brain" of the Houthis.