"I announce as minister of defence the toppling of the regime and detaining its chief in a secure place," said Awad Ibn Ouf in a televised address to the nation.
A transitional military council is now to replace the president for two years, said Ibn Ouf, adding that the country's borders and airspace would be shut until further notice.
After months of protests, #Sudan's military have arrested long-term leader Omar #AlBashir.The Debate – France 24 (@F24Debate) April 11, 2019
Earlier this Thursday, the country's defense minister announced that a military council will run the country for a two year transitional period.#F24Debate asks, what's next for Sudan? pic.twitter.com/e1zTo1GsVJ
The announcement came after months of street protests in Sudan calling for Bashir to go. But organisers of the demonstrations rejected his removal by the army as a "coup conducted by the regime" and vowed to keep up their campaign.
"The regime has conducted a military coup by bringing back the same faces and the same institutions which our people rose against," the Alliance for Freedom and Change said in a statement.
"We all reject what has been mentioned in the coup statement issued by the regime," said the alliance, an umbrella group of grass-roots organisers and opposition parties and rebel groups.
"We call on our people to continue their sit-in in front of army headquarters and across all regions and in the streets."
Bashir assumed power in a 1989 coup and was one of Africa's longest serving presidents.
During the morning, crowds rallied in the squares across the centre of Khartoum as the army promised an important announcement.
Chanting "the regime has fallen," thousands poured into the open ground outside army headquarters where protesters have braved tear gas to maintain a sit-in for six days.
The protests started in December over the government's tripling of the price of bread and escalated into the biggest challenge to Bashir's rule.
The security agency announced it was freeing all political prisoners.
Troops raided the offices of the Islamic Movement, the ideological wing of Bashir's ruling National Congress Party, witnesses told AFP. And martial music was played on state television as soldiers ordered the TV to halt its normal programming.