Media tycoon Mir Quasem Ali, 63, of Jamaat-e-Islam, was sentenced to death in 2014.
He had been convicted of offences including murder and torture.
The tycoon was hanged at a high-security prison outside Dhaka on yesterday evening.
He was arrested in 2010 and convicted in 2014.
He declined to seek a presidential pardon, which would have required an admission of guilt.
A huge security operation was staged before and after his execution.
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Previous executions have led to huge crowds demonstrating both in support of Jamaat-e-Islam leaders.
An ambulance carrying Ali’s body emerged from the jail in the early hours of today and took it to his home village in Manikganj for burial.
Ali’s wife Khandker Ayesha Khatun told reporters at the jail that the family wanted to bury him in Dhaka, but this request was refused by the authorities.
Charges
At his trial, Ali had been accused of involvement in a “reign of terror” in the city of Chittagong.
He was found guilty of eight of the 14 charges he faced including the abduction and killing of a teenager who supported the creation of a state independent from Pakistan.
“All along he said he was innocent. He said he is being killed unjustifiably,” Tahera Tasnim, one of his daughters told the AFP news agency.
She was among 23 family members who met him for the last time in the prison just hours before he was hanged.
Five Jamaat-e-Islam leaders have now been executed for war crimes since Prime Minister Sheikh Hasina set up a war crimes tribunal in 2010.
The International Crimes Tribunal (ICT) has so far sentenced 24 people to death and 18 to jail for varying terms on charge of genocide and crimes against humanity.
Critics of the court say the government has been using the ICT to target political opponents.
Human Rights Watch has previously said the court’s procedures do not meet international standards.
The Hasina regime has defended the trials, saying they are necessary to heal the wounds of the conflict.
PM Hasina of the secular Awami League Party has been running long campaign of brutally cracking down on Islamic groups peacefully opposing her regime.
