Election Commission figures said the BNP alliance had won 212 seats, compared with 77 for the Islamist-led Jamaat-e-Islami alliance -- which said Friday there had been "massive irregularities in vote counting" and demanded "redress".
It was unclear immediately what action Jamaat would take.
BNP chief Rahman told AFP two days before polling he was "confident" that his party -- crushed during the autocratic 15-year rule of ousted prime minister Sheikh Hasina -- would regain power in the South Asian nation of 170 million people.
Hasina's Awami League party was barred from taking part.
The US embassy congratulated Rahman and the BNP for a "historic victory", while neighbouring India praised Rahman's "decisive win", a significant step after recent rocky relations with Bangladesh.
China and Pakistan, which both grew closer to Bangladesh since the 2024 uprising and the souring of ties with India, where Hasina has sheltered since her ouster, also congratulated the BNP.
- 'Seek redress' -
But Jamaat chief Shafiqur Rahman, 67, who had mounted a disciplined grassroots campaign on a platform of justice and ending corruption, told reporters angrily on Friday that his party would "seek redress from the Election Commission".
His party had earlier claimed there were "repeated inconsistencies and fabrications" in the result announcement process.
"Our youths will not spare anybody who attempts to compromise the sacrifices made in July", he said, referring to the 2024 uprising against Hasina.
The Election Commission said turnout was 59 percent across 299 constituencies out of 300 in which voting took place.
Another 50 seats in parliament reserved for women will be named from party lists.
Heavy deployments of security forces are posted countrywide, and UN experts warned ahead of the voting of "growing intolerance, threats and attacks" and a "tsunami of disinformation".
Political clashes killed five people and injured more than 600 during campaigning, police records show.
However, after a turbulent campaign period, the vote passed largely peacefully -- and a day after the vote, Bangladesh has seemingly reacted to the result so far with calm.
Party workers spent the whole night after voting in front of the BNP offices.
"We will join the nation-building effort led by Tarique Rahman," Md Fazlur Rahman, 45, told AFP. "Over the last 17 years, we have suffered a lot."
Khurshid Alam, 39, a businessman in Dhaka, said: "The promises and aspirations for the next five years made by Tarique Rahman to the people -- I hope he can implement them."
- 'Ended the nightmare' -
Interim leader Muhammad Yunus, who will step down once the new government takes power, has urged all to stay calm.
"We may have differences of opinion, but we must remain united in the greater national interest," he said.
The 85-year-old Nobel Peace Prize winner has led Bangladesh since Hasina's rule ended with her ouster in August 2024.
Yunus said the election had "ended the nightmare and begun a new dream".
Hasina, 78, who was sentenced to death in absentia for crimes against humanity, issued a statement decrying an "illegal and unconstitutional election".
Yunus championed a sweeping democratic reform charter to overhaul what he called a "completely broken" system of government and to prevent a return to one-party rule.
Voters in Thursday's election also endorsed proposals in a referendum that included prime ministerial term limits, a new upper house of parliament, stronger presidential powers and greater judicial independence, with 60 percent backing the changes.
Crisis Group analyst Thomas Kean warned that the incoming government now faced "daunting challenges", including "boosting the economy, ensuring security and continuing the reform process".
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