Hasina will serve another five years in office as media reports show her party the Awami League and its allies have won 216 seats out of 299 while ballot counting continued in some constituencies late at night.
With the main opposition Bangladesh Nationalist Party, BNP, led by former premier Khaleda Zia boycotting the poll, Hasina's coalition is expected to win the remaining seats.
A final official declaration from the Election Commission is expected on Monday.
A total of about 120 million Bangladeshis were eligible to cast their ballots but turnout was just around 40 percent, Chief Election Commissioner Kazi Habibul Awal said after the polls closed.
Meanwhile, Zia called the poll a sham and refused to accept the outcome, saying Bangladeshi voters have rejected the one-sided election.
The elections were held amid tight security as the BNP and its allies had boycotted the vote and gave a two-day strike call. There were mass arrests of opposition leaders and supporters on Sunday.
According to a prominent rights group, nearly 10,000 activists were arrested after an opposition rally on 28 October turned violent, resulting in the deaths of at least 16 people and injuring more than 5,500. It accused the government of "filling prisons with political opponents".
The opposition parties also accuse Hasina of turning Bangladesh into a one-party state and silencing dissent and civil society. But authorities blame much of the violence on the BNP, accusing it of seeking to sabotage the election.
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