Motiur Rahman Nizami, 73, was executed early on Wednesday (local time), Law Minister Anisul Haq confirmed.
He had been convicted of genocide, rape and torture.
Nizami had led Bangladesh's largest Islamist party, Jamaat-e-Islami. Hundreds of people gathered near his prison in the capital Dhaka to celebrate the hanging.
Bangladesh says the prosecutions are needed to heal the wounds of conflict but human rights groups say the trials fall short of global standards and lack international oversight.
Last week, Nizami lost his final appeal against the sentence. He was hanged after refusing to seek mercy from President Abdul Hamid.
"Nizami has been deprived of justice," Jamaat's acting leader, Maqbul Ahmad, said. "He's a victim of political vengeance."
The party also called for a nationwide strike on Thursday.
Security was tightened across the country ahead of the execution.
Nizami is the fourth leader of the Jamaat-e-Islami party to have been executed since Prime Minister Sheikh Hasina set up a war crimes tribunal to look into abuses during the independence war.
A former government minister, Nizami was one of the most important figures to be found guilty.
He was convicted of setting up a militia which helped the Pakistani army identify and kill pro-independence activists.
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 reports.
The hanging comes amid a spate of killings of liberal activists, secularists, foreigners and members of religious minorities that the government has blamed on Islamists.