Army chief General Waker-Us-Zaman said in a televised address that Hasina 76, had left the country and that an interim government would be formed.
Media reports said she had flown in a military helicopter with her sister and was headed to the eastern Indian state of West Bengal just across the border. Another report said she was headed to India's northeastern state of Tripura.
Reuters could not immediately verify the reports.
Television visuals showed thousands of people pouring into the streets of the capital Dhaka in jubilation and shouting slogans. Thousands also stormed Hasina's official residence 'Ganabhaban', shouting slogans, pumping fists and showing victory signs.
Television visuals showed crowds in the drawing rooms of the residence, and some people could be seen carrying away televisions, chairs and tables from what was one of the most protected buildings in the country.
"She has fled the country, fled the country," some shouted.
Protesters in Dhaka also climbed atop a large statue of independence leader Sheikh Mujibur Rahman, Hasina's father, and began chiselling away at the head with an axe, the visuals showed.
Student activists had called for a march to the capital Dhaka on Monday in defiance of a nationwide curfew to press Hasina to resign, a day after deadly clashes across the country killed nearly 100 people. About 150 people were killed in protests last month.
On Monday, at least six people were killed in clashes between police and protesters in the Jatrabari and Dhaka Medical College areas on Monday, the Daily Star newspaper reported. Reuters could not immediately verify the report.
Bangladesh has been engulfed by protests and violence that began last month after student groups demanded scrapping of a controversial quota system in government jobs.
That escalated into a campaign to seek the ouster of Hasina, who won a fourth straight term in January in an election boycotted by the opposition.
(Reporting by Ruma Paul and Sudipto Ganguly; Writing by YP Rajesh; Editing by Raju Gopalakrishnan)

Students shout slogan as they take part in a demonstration during the first day of non-cooperation movement at the Raju Memorial Sculpture, Dhaka University campus in Dhaka, Bangladesh, 04 August 2024. The Anti-Discrimination Student Movement organizers are demanding the resignation of the current government. Dhaka authorities have imposed a new curfew starting 06:00 p.m. local time on 04 August. As casualties mounted and law enforcement struggled to contain the unrest, the Bangladeshi government on 20 July 2024 had imposed an initial nationwide curfew and deployed military forces after violence broke out in Dhaka and other regions following student-led protests demanding reforms to the government's job quota system. EPA-EFE/MONIRUL ALAM