Motiur Rahman Nizami, 72, was hanged early yesterday morning (local time) on Wednesday, law minister Anisul Haq said.
Nizami led the Bangladeshi wing of Jamaat-e-Islami, and he lost his final appeal against the sentence last week.
He was convicted of genocide, rape and torture; charges the defence said were not proven beyond reasonable doubt.
Security was tightened across the country ahead of the execution.
Supporters of Nizami protested outside Dhaka’s Central prison, where the sentence was carried out.
Nizami is the fourth leader of Jamaat-e-Islami to have been executed since Prime Minister Sheikh Hasina set up a war crimes tribunal to look into abuses during the independence war.
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A former government minister, Nizami was one of the most prominent figures to be found guilty.
He was convicted of setting up a militia which helped the Pakistani army identify and kill pro-independence activists.
Supporters and rights groups say the executions are politically motivated.
Nizami will be buried in his village home in the northern part of Bangladesh.
His family met him briefly before his execution but left without speaking to the media, Bangladesh’s Daily Star reported.
Prime Minister Sheikh Hasina of the Awami League party has been running long campaign of brutally cracking down on Islamic groups peacefully opposing her secular regime.
There will be a funeral procession for Motiur Rahman today at Altab Ali Park, east London at 2pm.
