Law Minister Anisul Haq told the BBC that the president would issue an ordinance on Tuesday making it law.
There was widespread outrage in Bangladesh last week after footage of a brutal gang assault on a woman went viral on social media.
An activist group says it recorded about 5,400 rape cases last year.
But activists say conviction rates are extremely low and many cases go unreported because women fear they will be stigmatised. Protesters galvanised by last week’s viral video have demanded faster trials and changes to the way rape cases are prosecuted.
An investigation by Bangladesh’s National Human Rights Commission found that the woman in the viral video, who was attacked in the southeastern district of Noakhalim, had been raped repeatedly over time and terrorised. Eight men were arrested after the video emerged.
In a separate case another woman was allegedly gang raped last week in a hostel in the northern district of Sylhet, leading to the arrest of several members of the student wing of the ruling party.
Bangladesh was rocked over the weekend by an unprecedented level of protest. Demonstrators carried signs reading “Hang the rapists” and “No mercy to rapists”. In the capital Dhaka, a mock gallows was erected by protesters.
Responding directly to the protests, the government decided to make the change by way of an ordinance, since parliament is not sitting – effectively passing it directly into law.