Kushayb, a senior Janjaweed commander in the early years of the conflict, was the target of a 2007 ICC arrest warrant on multiple counts including rape, murder and pillaging.
Hassan al-Senousi, another displaced Darfuri at the Al-Sarif camp near South Darfur's regional capital Nyala, said Kushayb's arrest brought him "deep satisfaction".
Kushayb's arrest comes less than a year after a transitional government took power following Bashir's ouster by the military in April 2019 on the back of vast protests against his rule.
Kushayb is set to be the first of five Sudanese suspects wanted by the ICC over atrocities in Darfur to appear before the court.
"Kushayb's arrest is a success for international justice and... for the victims," Minni Minnawi, leader of a rebel group active in Darfur Sudanese Liberation Army, wrote on Twitter.