Tens of thousands of demonstrators in the capital, Dhaka, cheered the news.
The legal amendment also paves the way for the prosecution and potential ban of the Jamaat-e-Islami party.
Jamaat chief Abdul Kader Mullah was given life for his alleged role in crimes in the 1971 independence war.
The ruling sparked nearly two weeks of angry mass protests in Dhaka and other cities.
Demonstrators - mainly young men and women - demanded the death penalty for Mullah and 10 others accused of committing crimes against humanity during the country's war of independence war with Pakistan in 1971.
The announcement comes a day after three people were killed in clashes between police and Jamaat supporters.
The Jamaat has called for a country-wide general strike on Monday in protest at the deaths.Bitter rivals
On Sunday, tens of thousands of protesters gathered in a busy intersection of Dhaka burst into cheers after the Bangladeshi parliament approved the changes to the existing law, the BBC's Anbarasan Ethirajan reports from the capital.
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Bangladesh independence war, 1971
Civil war erupts in Pakistan, pitting the West Pakistan army against East Pakistanis demanding independence
Fighting forces an estimated 10 million East Pakistani civilians to flee to India
In December, India invades East Pakistan in support of the East Pakistani people
Pakistani army surrenders at Dhaka and its army of more than 90,000 become Indian prisoners of war
East Pakistan becomes the independent country of Bangladesh on 16 December 1971
Key defendants
Article that changed history
Scars of war 40 years on
Bangladesh confronts war crimes
The government and others can now appeal against verdicts at the International Crimes Tribunal, set up in 2010 to try those Bangladeshis accused of collaborating with Pakistani forces and committing atrocities during the war, our correspondent says.
The amendment will also give powers to the special tribunal to prosecute any organisations or political parties allegedly involved in war crimes.
If found guilty, the party "can be banned" from politics, law minister Shafique Ahmed said.
Critics say the provision is aimed at the Jamaat, which opposed Bangladesh's independence from Pakistan, our correspondent reports.
The Islamist party says the latest changes to the law is nothing but an attempt by the government to destroy the party.
Eight of the accused are Jamaat party leaders, while the remaining two are members of the opposition Bangladesh Nationalist Party (BNP), one a former minister.
Jamaat is an ally of the BNP, bitter political rivals of current Prime Minister Sheikh Hasina, who has made prosecuting war crimes a key goal of her government.
Human rights groups have said the tribunal falls short of international standards. Jamaat and the BNP accuse the current government of pursuing a political vendetta through the tribunal.
Official estimates say more than three million people were killed in the 1971 war which resulted in independence from Pakistan.
