BBC:
President Shahabuddin said he had chaired a meeting of army chiefs and political representatives.
He said an interim government would be formed, new elections called and a national curfew lifted.
In Dhaka on Monday, police and other government buildings were attacked and set on fire. Protesters attempted to tear down a statue of independence leader Sheikh Mujibur Rahman, Ms Hasina’s father.
Army and police units were deployed across the city. Mobile phone service was reportedly cut off for several hours before being restored.
On Monday, protesters were seen carrying out furniture from the prime minister’s residence.
Dozens were reported killed on Monday, although the precise toll remained unclear. The AFP news agency reported the toll as 66 dead, though local outlet the Dhaka Tribune said as many as 135 had been killed.
Ms Hasina’s departure leaves a vacuum in Bangladeshi politics, which has long been characterised by a rivalry between her Awami League and the Bangladesh Nationalist Party.
The country has experienced several military coups, most recently in 2007.
The US commended the army for its “restraint” and said an interim government should be formed. The EU urged an “orderly and peaceful transition” towards a democratically elected government.
There was no official reaction from neighbour and regional power India.
