After hours of anticipation following news that Mr Al Bashir "stepped down", Defence Minister Awad Mohamed Ahmed ibn Auf - who was appointed Vice President two months ago - announced on state television that he will head a military transitional government for the next two years.
Defense Minister Awad ibn Auf also announced the imposition of a one-month curfew and a three-month state of emergency in a televised statement.
He added that al-Bashir has been arrested and is in a safe place.
Mr Ibn Auf announced a state of emergency, a nationwide ceasefire and the suspension of the constitution.
Al Jazeera's Hiba Morgan, reporting from the Sudanese capital, Khartoum said there was a heavy security presence on the city's main roads.
The UN chief voiced his "expectation that the democratic aspiration of the Sudanese people will be realised through an appropriate and inclusive transition process", said his spokesman Stephane Dujarric.
Protesters have called for a civilian government. Sayda Elsir, a demonstrator in the sit-in, said that everyone around her was outraged when they heard the announcement.
Sudanese protesters have vowed to keep up demonstrations, rejecting the army's move.
Aside from the fact that they are all hard-working, extremely well educated and successful, the other thing they have in common is that they - or their families - all fled Sudan as a result of the 1985 overthrow of the Numairi regime, which was inspired by Islamist leader Hassan Al-Turabi, who for long was Al-Bashir's religious backer.
A young woman who became a symbol of the protests also dismissed the military announcement.
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Tens of thousands of demonstrators were massed at a sit-in they have held for almost a week outside the military's headquarters in central Khartoum, the capital.
"We finally win this battle, we struggled a lot and we suffered a lot but everything (is) supposed to have an end", 45-year-old tea seller Fathia Imam told Al Jazeera at the square of the sit-in.
LATEST from a 2nd insider: there is now a meeting underway at the Military Command HQ between spy chief Gosh, RSF/Janjaweed leader Hemidti, Defence minister & current VP Awad Ibn Auf & head of the police, discussing who will lead transitional High Council of Armed Forces.
Observers say although it remains unclear what the armed forces will announce, it appears as though the army has made a decision to support the protesters. "We will only accept a transitional civilian government", Mr Sennar told Reuters.
Protesters celebrate in Khartoum, Sudan.
While recent events in Algeria and Sudan have been unique to those countries, analysts say the rapid downfall Bouteflika and Bashir are a warning to authoritarian leaders in the region that they will ignore popular anger, especially over economic grievances, at their peril.
Soldiers stormed the headquarters of Mr Bashir's Islamic Movement, the main component of the ruling National Congress Party. He said that all political prisoners would be released and stated that a curfew would be imposed from 6 PM to 4 AM.
Mr Bashir, a former paratrooper who seized power in a bloodless coup in 1989, has been a divisive figure who has managed his way through one internal crisis after another while withstanding attempts by the West to weaken him.
Sudanese expats living overseas would tell stories of how everything changed after Al-Turabi began injecting his extremist views into society and Al-Bashir endorsed them with an iron fist.
Washington followed up with sanctions four years later.
Outside army headquarters, dozens of joyful protesters early Thursday climbed on top of land-cruisers and armoured vehicles that had been posted to protect them from intervention by other branches of the security forces.