Jibril, 68, died in Cairo where he had been hospitalised for two weeks, said Khaled al-Mrimi, secretary of the Alliance of National Forces Party founded by Jibril in 2012.
He had been admitted to the Ganzouri Specialised Hospital in Cairo on March 21 after suffering from cardiac arrest and three days later tested positive for coronavirus, hospital director Hisham Wagdy said.
"He started... recovering the day before yesterday but then he began deteriorating again", Wagdy told AFP in Cairo, confirming that Jibril died at 2:00 pm.
Jibril headed the rebel National Transitional Council (NTC), the interim government during the NATO-backed rebellion that toppled and killed Kadhafi.
He had been an economic adviser to the Qadhafi regime in its final years, before joining the revolution in 2011 and briefly serving as premier.
Jibril resigned three days after Kadhafi was captured and killed when NTC fighters overran his hometown Sirte on October 20, 2011.
In the early days of the Libyan uprising, Jibril made several trips abroad to rally European and US support for the rebels against Kadhafi.
In 2012, after the veteran leader was ousted and killed, Jibril stood in the country's first ever democratic elections and his party won the vote but failed to clinch a majority in parliament which chose an independent candidate to become prime minister.
Amid the chaos and violence that erupted in the following years, Jibril left Libya to live abroad.
Libya, now divided between a UN-recognised government based in Tripoli and a rival administration in the country's east, announced its first death from coronavirus earlier this week.
Health authorities said an 85-year-old woman was confirmed to have had COVID-19 on examination after her death, without giving further details.
The UN-recognised Government of National Accord which controls the west of the country has officially recorded 10 cases.
No cases have been declared in the south and east, which are largely under the control of the rival administration supported by military strongman Khalifa Haftar who has been battling to seize Tripoli.
Wagdy, the hospital director in Cairo, said that Jibril was in and out of consciousness during his time in the hospital's intensive care unit, where he had been quarantined since his admission.
Mrimi said that Jibril had appeared in stable conditions in recent days "and was even getting ready to leave the hospital" before his condition deteriorated again.