His visit is part of a regional tour following an accord between Israel and the UAE this month to forge full relations and comes as Israel and the United States push more Arab countries to follow.
"Happy to announce that we are on the FIRST official NONSTOP flight from Israel to Sudan!" Pompeo said on Twitter after taking off from Tel Aviv.
Pompeo will meet Sudan's prime minister and the head of its ruling council during a brief stopover in Khartoum to discuss U.S. support for the civilian-led government and for "deepening the Sudan-Israel relationship," according to the State Department.
The United States has been restoring its own ties with Sudan following the ouster of former Islamist leader Omar al-Bashir in April 2019, and is pushing to be removed from the list of countries that Washington considers state sponsors of terrorism.