Latest counts in an election seen as the South Asian nation's first truly competitive in years gave the BNP and its allies at least 212 of the 299 seats up for grabs, domestic TV channels said on Friday.
The opposition Jamaat-e-Islami and its allies won 70 seats in the Jatiya Sangsad, or House of the Nation.
The BNP, which returns to power after 20 years, thanked the people soon after winning a majority in the overnight vote count and called for special prayers on Friday for the nation and its people.
"Despite winning ... by a large margin of votes, no celebratory procession or rally shall be organised," the party said in a statement calling for prayers nationwide.
A clear outcome had been seen as key for stability in the Muslim-majority nation of 175 million after months of deadly anti-Hasina unrest disrupted everyday life and industries such as garments, in the export of which Bangladesh is No.2 globally.
BNP leader Tarique Rahman is widely expected to be sworn in as prime minister.
The son of the party's founder, former president Ziaur Rahman, he returned in December to the capital, Dhaka, from 18 years abroad.
Nobel peace laureate Muhammad Yunus, 85, held office as interim head after Hasina fled to neighbouring India in August 2024.
Now in exile in New Delhi, Hasina long dominated Bangladesh politics along with Rahman's mother, Khaleda Zia, while his father was a leading independence figure who ruled from 1977 to 1981 before he was assassinated.
Manual counting of paper ballots will run until at least noon on Friday, officials said, since starting on Thursday immediately after polls closed.
The BNP win with more than 200 seats is one of its biggest, surpassing its 2001 victory with 193, although Hasina's Awami League, which ruled for 15 years and was barred from contesting this time, secured a bigger tally of 230 in 2008.
But bigger tallies for both parties in elections of other years were widely seen as one-sided, boycotted or contentious.
Night-time throngs of supporters cheered and shouted slogans at the BNP headquarters in Dhaka as the scale of the party's landslide became clear.
The head of its main rival, the Islamist Jamaat-e-Islami, conceded defeat and vowed his party would not engage in the "politics of opposition" just for the sake of doing so.
"We will do positive politics," Shafiqur Rahman told reporters.
However, the National Citizen Party, led by youth activists who played a key role in toppling Hasina and was a part of the Jamaat-led alliance, won just five of the 30 seats it contested.
Turnout appeared on track to exceed the 42 per cent of the previous election in 2024, with media saying more than 60 per cent of registered voters were expected to have taken part.
More than 2000 candidates, many independents among them, were on the ballot, which featured a record number of at least 50 parties.
Voting in one constituency was postponed after a candidate died.
Broadcaster Jamuna TV said more than two million voters chose "Yes", while more than 850,000 said "No" in a referendum on constitutional reforms held alongside the election, but there was no official word on the outcome.
The changes include two-term limits for prime ministers and stronger judicial independence and women's representation.
