Analysts say a decisive result is crucial for steady governance in the nation of 175 million, as the deadly anti-Hasina protests triggered months of unrest and disrupted key industries, including the huge garments sector, the world's second-largest exporter.
It is the world's first election after an uprising led by under-30s, or Gen Z, to be followed by Nepal in March.
The contest pits two coalitions led by former allies, the Bangladesh Nationalist Party (BNP) and the Islamist Jamaat-e-Islami, with opinion polls giving an edge to the BNP.
In Dhaka, the capital, people queued up outside voting booths before polls opened on Thursday morning, including eager participants such as Mohammed Jobair Hossain, 39, who said he last voted in 2008.
"I am feeling excited because we are voting in a free manner after 17 years," Hossain said.
"Our votes will matter and have meaning."
Hasina's Awami League is banned, and she remains in self-imposed exile in long-term ally India, opening the window for China to expand its influence in Bangladesh as Dhaka's ties with New Delhi deteriorate.
Elections were held during Hasina's tenure but they were marred by opposition boycotts and intimidation, critics have said.
This time more than 2000 candidates, including many independents, are vying for 300 seats in the Jatiya Sangsad, or House of the Nation.
Voting in one constituency has been postponed due to the death of a candidate.
At least 50 parties are contesting in total, a national record.
"This election is not just another routine vote," Nobel laureate Muhammad Yunus, head of an interim government installed after Hasina's ouster, said this week.
"The public awakening we witnessed against long-standing anger, inequality, deprivation and injustice finds its constitutional expression in this election."
In parallel, there will be a referendum on a set of constitutional reforms, including increasing women's representation, strengthening judicial independence and imposing a two-term limit on the prime minister.
Despite the crowded field and expectations of a close race, the campaign period remained largely peaceful, barring a few incidents.
About 958,000 personnel from the police, army and paramilitary forces were deployed throughout the country on election day, the Election Commission said.
Police and army personnel were stationed outside most polling booths.
Counting will begin soon after polls close in the late afternoon, with early trends expected about midnight and results are likely to be clear by Friday morning.
Nearly 128 million people are registered to vote, with 49 per cent of them women, but only 83 female candidates are contesting.
Nearly half of the total electorate is aged between 18-35, with many of them first-time voters.
The two prime ministerial candidates are the BNP's Tarique Rahman and Jamaat chief Shafiqur Rahman.
They are not related.
Several voters are conflicted about taking part in the election, but some are determined to cast their ballots.
"During Hasina's time, we couldn't cast our votes," said Shakil Ahmed, a driver.
"It's my right to vote. This time, I won't miss it."
