Ms Hasina, 76, had already left the country to a "safer place", one of her advisers said, before crowds arrived at her palace.
The resignation came a day after at least 90 people were killed and hundreds injured in a new round of demonstrations.
The unrest in Dhaka and elsewhere began with a demand to abolish quotas in civil service jobs but escalated into a mass anti-government movement.
Getty Images Protesters are blocking the Shahbagh intersection during a protest in Dhaka, Bangladesh, on August 4, 2024, to demand justice for the victims arrested and killed in the recent nationwide violence during anti-quota protests. Getty Images
Protesters blocked a motorway in Bangladesh's capital city
Entrances to Dhaka were blocked on Monday, with army units and police deployed across the city.
The internet was also completely shut down before being restored a few hours later.
The government had also announced a three-day "holiday" - widely interpreted as a curfew - which closed down businesses and the courts.
However, this did not stop tens of thousands of people from converging on the city, heeding a call by protest leaders to start a "long march to Dhaka". Anger was high following the deaths - mostly of protesters - on Sunday.
Both police and some supporters of the governing party were seen shooting at anti-government protesters with live ammunition. Police also used tear gas and rubber bullets.
Thirteen police officers were also killed on Sunday when thousands of people attacked a police station in the district of Sirajganj, police said. Two more police died of their injuries on Monday following the attack. Elsewhere there were reports of several more protesters being killed.
The total death toll from weeks of unrest now stands at some 300, most of them protesters shot by security forces.
Mobile operators received orders from the government to shut off their 4G services on Monday, reports said.
The country is "again in the midst of a near-total national internet shutdown after earlier social media and mobile cuts", said NetBlocks, a watchdog that monitors internet freedom.
On 18 July, the Bangladeshi government had also switched off the country's mobile internet in an attempt to quell the protests. Broadband connectivity was restored a week later, while mobile internet services came back online days after.
But neither the internet blackout nor an indefinite nationwide curfew imposed on Sunday have hindered the protesters across Bangladesh.
On Monday, thousands of protesters started marching in Uttara, a suburb of Dhaka, chanting and demanding Ms Hasina's resignation - under the watchful eye of army personnel and police officers who have been stationed across various points in the capital.
Amid calls for her resignation, Ms Hasina initially sounded defiant. Speaking after a meeting with security chiefs on Monday, she said the protesters were "not students but terrorists who are out to destabilise the nation".
On Sunday, Law and Justice Minister Anisul Huq told the BBC’s Newshour programme that authorities were showing “restraint”.
“If we had not shown restraint, there would have been a bloodbath. I guess our patience has limits,” he added.
Bangladesh blocks internet as more violence and protests expected
Why is the Bangladeshi government facing so much anger?
Deaths and injuries have also been reported across the country, including the northern districts of Bogra, Pabna and Rangpur.
On Sunday, thousands of people gathered in a main square in Dhaka and there were violent incidents in other parts of the city.
“The whole city has turned into a battleground,” a policeman, who asked not to be named, told the AFP news agency. He said a crowd of several thousand protesters had set fire to cars and motorcycles outside a hospital.
Asif Mahmud, a leading figure in the nationwide civil disobedience campaign, called on protesters to march on Dhaka on Monday.
"The time has come for the final protest," he said.
Students Against Discrimination, a group behind the anti-government demonstrations, urged people not to pay taxes or any utility bills.
The students have also called for a shutdown of all factories and public transport.
Around 10,000 people have been reportedly detained in a major crackdown by security forces in the past two weeks. Those arrested included opposition supporters and students.
Some ex-military personnel have expressed support for the student movement, including ex-army chief General Karim Bhuiyan, who told journalists: “We call on the incumbent government to withdraw the armed forces from the street immediately.
He and other ex-military personnel condemned "egregious killings, torture, disappearances and mass arrests".
Some of the wounded were driven away by protesters
The protests began when students took to the streets last month over a quota that reserved one third of civil service jobs for relatives of the veterans of Bangladesh’s independence war with Pakistan in 1971.
Most of the quota has now been scaled back by the government following a Supreme Court ruling, but students have continued to protest, demanding justice for those killed and injured, and for Ms Hasina to step down.
Earlier, Ms Hasina offered unconditional dialogue with the student leaders.
“I want to sit with the agitating students of the movement and listen to them. I want no conflict," she said.
But the student protesters have rejected that offer.
Bangladeshi media say most of those killed in last month’s protests were shot dead by police. Thousands were injured.
The government has argued that police opened fire only in self-defence and to protect state properties.
