Defence Minister Ahmed Awad Ibn Auf says transitional military council will rule for two years.
Sudanese president Omar al-Bashir has stepped down after months of protests, according to government sources.
A military council is expected to replace him.
On Thursday, anti-government protesters marched through the streets of Khartoum chanting anti-Bashir slogans.
Protesters outside the defence ministry chanted: "It has fallen, we won."
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UPDATE: Sudan's President Omar al-Bashir is under arrest "in a safe place" and a military transitional council has been put in place, Sudan's defence minister and army general has said.
Ahmed Awad Ibn Auf declared a three month state of emergency and said the military council will rule for two years.
He said airspace will be closed for 24 hours.
Tens of thousands of Sudanese marched early on Thursday through the centre of the capital Khartoum in jubilation, dancing and chanting anti-Bashir slogans.
Protesters outside the defence ministry chanted: "It has fallen, we won."
The Sudanese army had said in the early hours of Thursday morning that it will make "an important announcement", after months of protests against the longtime leader.
"The Sudanese army will issue an important statement soon. Wait for it," a television anchor on state TV said, without giving further details.
The protests, which erupted in December, have become the biggest challenge yet to Bashir's three decades of rule.
Thursday also marked the sixth day of a defiant sit-in outside the military's headquarters, which also houses Bashir's official residence and the defence ministry.
Agencies