Senior US officials say President Donald Trump sealed the deal during a phone call with Israeli Prime Minister Benjamin Netanyahu and Sudanese Prime Minister Abdullah Hamdouk and Interim Council Chairman Abdel Fattah al-Burhan.
As part of the agreement, Donald Trump took steps to remove Sudan from the US government's list of countries promoting terrorism.
The senior US official said Donald Trump signed the document into Air Force One on Thursday night to inform Congress of his intention to remove Sudan from the list.
"The leaders agreed to normalize relations between Sudan and Israel and to end the war between their nations," a joint statement issued by the three countries said.
Sudan is the third Arab country in the past two months to declare an end to hostilities with Israel and normalize relations.
Earlier, the United Arab Emirates and Bahrain agreed to normalize relations with Israel.
The United States negotiated the deal with Jared Kushner, Donald Trump's senior adviser and son-in-law, Evie Berkowitz, the Middle East envoy, Robert O'Brien, the national security adviser, Mike Pompeo, the foreign secretary, and Miguel Correa, the national security official.
"Obviously this is a major step forward in establishing peace between Israel and Sudan. Making peace agreements is not as easy as we see it right now, it is very difficult," Jared Kishner told Reuters.
Officials say a signing ceremony between Sudan and Israel is expected at the White House in the coming weeks.
The leaders agreed to establish economic and trade ties, with a focus on agriculture, the joint statement said.
The statement said that a delegation from each country would meet in the coming weeks to discuss agreements on cooperation in the fields of agricultural technology, aviation, refugee issues and other areas.
According to the statement, Sudan's interim government has shown courage and determination to fight terrorism, build democratic institutions and improve relations with its neighbors.
As a result, the United States and Israel agreed to partner with Sudan in its new beginning to ensure that it is fully recognized in the international community.
Jared Kishner called the normalization agreements the beginning of a "revolution" in the Middle East.
He said Sudan's decision was symbolic because in 1967, in its capital, Khartoum, the Arab League decided not to recognize Israel.
