The announcement on Twitter by the kingdom's foreign ministry on Sunday came after a meeting in Riyadh between King Salman and the recently appointed head of Sudan's transitional sovereign council General Abdel Fattah al-Burhan and Sudanese Prime Minister Abdalla Hamdok.
The designation as a state sponsor of terrorism dates back to 1993, over allegations that former President Omar al-Bashir's government was supporting groups deemed by the US to be "terrorist".
A transitional government was installed in August following months of mass protests that led to the military overthrowing al-Bashir in April.
Inclusion on the terror list makes Sudan ineligible for desperately-needed debt relief and financing from lenders such as the International Monetary Fund and the World Bank. Removal would potentially open the door for foreign investment.
Asmaa Abdalla, Sudan's foreign minister, told Al Jazeera last month that the resolution of the issue was the new government's top priority.
In late September, Hamdok, a veteran economist, said he had held useful talks with US officials on the topic and expressed hope that an agreement could be reached "very soon".
"Therefore we call on the United States to remove Sudan from the list of state sponsors of terrorism and to stop punishing the people of Sudan for crimes committed by the former regime," he said.
A senior US official said in August that Washington would test the commitment of Sudan's new transitional government to human rights, freedom of speech and humanitarian access before it agrees to remove the country from the state sponsor of terrorism list.
Observers have previously said that it is unlikely that the US is going to recommend any changes in the status of Sudan until elections are held, a new constitution is formed and a permanent civilian government has been established.
Comprising military and civilian members who were sworn in in August, the sovereign council is to rule Sudan for a little over three years until elections can be held.
Separately, Saudi Arabia's foreign ministry said on Sunday that Riyadh was also working on initiating investments in Sudan and improving existing projects.
It also said on Twitter that Sudan was working on supporting Saudi Arabia in international forums, providing an environment for investment and expanding its agricultural sector.
Al Jazeera's Hiba Morgan, reporting from Sudan's capital, Khartoum, said Sunday's visit came just days after Hamdok met the Saudi delegation at the UNGA.
"At the Assembly, he said that Sudan does not need aid from Saudi Arabia, what it needs is economic development," she said.
"When Sudan's President Omar al-Bashir was toppled in April, Saudi Arabia stepped in and announced that it would be giving $3bn in aid as well as donating fuel and wheat to try to curb the economic crisis in the country," she added.
Morgan noted that some Sudanese were worried about Saudi Arabia's interference.
"They think that Saudi Arabia played a big role, urging the military to attack protesters on June 3 [during a bloody crackdown on a Khartoum sit-in that had become the focal point of the pro-democracy protesters' struggle for a civilian-led government]," she said.
"We have also heard the prime minister saying repeatedly that there is a strategic alliance between Saudi Arabia and Sudan, and that's what he looks forward to developing and to make sure that the ties remain on economic levels and mutual interests between the two countries," she added.
Sudan is participating in the Saudi-UAE-led military coalition fighting Yemen's Houthi rebels. It has contributed some 10,000 soldiers to the coalition fighting on the ground, in a war that has killed tens of thousands of civilians and caused what the UN calls the world's worst humanitarian crisis.