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5 year oldSpeaking on state TV, Awad Ibn Ouf said the army had decided to oversee a two-year transitional period followed by elections.
He also said a three-month state of emergency was being put in place.
Protests against Mr Bashir, who has governed Sudan since 1989, have been under way for several months.
Mr Ibn Ouf said the "regime" was being removed and Mr Bashir would be kept in a safe place.
He said Sudan's constitution was being suspended, border crossings were being closed until further notice and airspace was being closed for 24 hours.
Mr Bashir is the subject of an international arrest warrant issued by the International Criminal Court (ICC), which accuses him of organising war crimes and crimes against humanity in Sudan's western Darfur region.
However it is unclear what will happen to him following his arrest.
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