Hasina's ruling Awami League party and its allies won 288 seats in the 300-seat parliament, with the main opposition securing only six, according to the Election Commission secretary Helal Uddin Ahmed.
However, the opposition alliance led by the Bangladesh National Party (BNP), has called on the country's election commission to void the results. It accuses Hasina's party of using stuffed ballot boxes and other illegal means to fix the result.
BNP spokesman Syed Moazzem Hossain Alal said there were "irregularities" in 221 of the 300 seats contested.
"We are demanding that a fresh election is held under a neutral government as early as possible," Kamal Hossain, who heads the alliance, told reporters.
Police say 21 people have died in election violence since the ballot was announced on 8 November.
Thirteen people were killed in clashes between Awami League and BNP supporters on Sunday, while three men were shot by police who said they were protecting polling booths.
An auxiliary police member was also killed by armed opposition activists, according to officials.
The opposition claims some 15,000 of its activists were detained during the campaign, crushing its ability to mobilise support.
Rights groups have accused Hasina's administration of stifling freedom of speech by toughening a draconian anti-press law and the enforced disappearance of dissenters.
Hasina rejects accusations of authoritarianism.