Rahman, the son of former premier Khaleda Zia and assassinated former president Ziaur Rahman, faces immediate challenges in restoring political stability, reviving investor confidence and rebuilding key industries after prolonged turmoil that followed the collapse of former prime minister Sheikh Hasina's government in 2024.
An interim government led by Nobel laureate Muhammad Yunus has been in charge since then.
The official count in a vote viewed as the South Asian nation's first truly competitive election in years gave the BNP and its allies at least 212 of the 299 seats up for grabs, the Election Commission said on Friday.
The opposition Jamaat-e-Islami and its allies won 77 seats in the Jatiya Sangsad, or House of the Nation.
Rahman, 60, has not yet commented even though more than 12 hours have passed since trends in favour of his party became clear, but the BNP asked people to refrain from large celebrations and offer special prayers on Friday instead.
He did not speak to media gathered outside his house in Dhaka, smiling and waving from his vehicle when he left for a mosque, local media reported.
"Despite winning ... by a large margin of votes, no celebratory procession or rally shall be organised," the party said.
The National Citizen Party (NCP), led by youth activists who played a key role in toppling Hasina, won just five of the 30 seats that it contested.
The NCP was part of the Jamaat-led alliance.
A clear outcome had been viewed as key for stability in the Muslim-majority nation of 175 million after months of deadly anti-Hasina unrest disrupted everyday life and industries including garment manufacturing.
Bangladesh is the No.2 exporter of apparel in the world.
Indian Prime Minister Narendra Modi, Pakistan Prime Minister Shehbaz Sharif and the US ambassador to Bangladesh, Brent T Christensen, were among the first to congratulate Rahman on his party's victory.
India, China and the United States are vying for influence in Bangladesh, with the US ambassador telling Reuters earlier this week that Washington was concerned about growing Chinese influence in the country.
New Delhi-Dhaka relations have nosedived since Hasina fled and took refuge in India.
The Jamaat-e-Islami conceded defeat late on Thursday night once trends became clear, but said on Friday it was "not satisfied" with the process and asked its followers to remain patient.
The party won its highest-ever tally of 70 seats in parliament, contesting for the first time since it was banned in 2013.
The ban was lifted after Hasina's ouster.
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 elections of other years were boycotted by one of the main parties or were contentious.
Turnout this time exceeded the 42 per cent of the last election in 2024, with media reports saying nearly 60 per cent of registered voters took part in the election on Thursday.
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.
