In an address on state television, Defence Minister Awad Mohamed Ahmed Ibn Auf announced a two-year period of military rule to be followed by presidential elections.
It also called on demonstrators to remain in the streets "until power is handed over to a civilian government that reflects the will of the revolution".
This political insider says that Sudanese Army's Chief of General Staff Lieutenant General Kamal Abdel-Marouf is their top choice to head the transitional council.
Cairo voiced its full belief in "the ability of the brotherly Sudanese people and their loyal national army to overcome the challenges of this critical stage.in order to achieve stability, prosperity and development", a foreign ministry statement said.
Al-Bashir had always been a pariah in many countries and he's even wanted by the global war crimes tribunal for atrocities in Darfur.
Protesters gathered in front of the military headquarters as military vehicles were deployed on key roads and bridges in Khartoum.
Shortly afterwards, thousands of demonstrators packed the streets of central Khartoum, their mood turning from jubilation at Bashir's expected departure to anger at the announcement of a military-led transition, a Reuters witness said.
Al-Bashir's fall came just over a week after Algeria's long-ruling, military-backed president, Abdelaziz Bouteflika, was driven from power.
Two officials in high positions in Sudan's government and military, told the AP that the military was in talks about a transitional government after forcing al-Bashir to step down.
The Hague-based International Criminal Court in 2009 indicted al-Bashir for alleged war crimes and crimes against humanity in Sudan's western province of Darfur. "After 30 years of the rule, we'll still be at a sit-in, until our demands are responded to with a transitional civil government, for a free, democratic, stable Sudan", she said.
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Sudan has suffered prolonged periods of isolation since 1993, when the United States added Bashir's government to its list of terrorism sponsors for harbouring Islamist militants.
The protests in Sudan have finally led to Omal al-Bashir stepping down and being placed under house arrest in what is undoubtedly a historic moment for Sudan.
For months, protesters rallied against rising food prices.
"Our demands are clear: We don't want to replace a coup with a coup", al-Mahdi said.
Sudanese security forces killed at least 14 people on Tuesday, NPR previously reported. It called on protesters to maintain a sit-in outside the defense ministry that started on Saturday, a source with the group said.
They vowed to continue the protest even though a curfew has been imposed as part of the three-month state of emergency. The military has taken over national TV and radio and arrested a number of former and current top leaders.
"We are waiting for big news", one protester told AFP from the sit-in.
Activist Alaa Salah tweeted: "AL-BASHIR IS OUT!"
Bashir was born on January 1, 1944 to a poor farming family in Hosh Bannaga, a small village consisting mainly of mud houses and dusty streets on the eastern bank of the Nile River, some 150 km (93 miles) north of the capital Khartoum.