Trump also said that Sudan has provided assurances it will not support acts of international terrorism in the future.
"I hereby certify, with respect to the rescission of the determination of 12 August 1993, regarding Sudan that: the Government of Sudan has not provided any support for acts of international terrorism during the preceding", Trump said in the letter on Monday.
Last week, Trump announced that the United States was going to remove Sudan off its State Sponsors of Terrorism list after Khartoum paid $335 million to US terrorism victims and their families.
In late September, Khartoum and Washington reportedly reached a deal that Sudan would sign a peace treaty with Israel in exchange for being excluded from the US State Sponsors of Terrorism list.
On Friday, Trump said that Israel and Sudan agreed to normalise relations in the latest step toward building peace in the Middle East.
Sudan will be the third Arab country, after the United Arab Emirates and Bahrain, to join Trump's Abraham accords - a system of fresh peace deals with Israel - and the fifth to have diplomatic relations with the Jewish state, together with Egypt and Jordan.