Ali was hanged in Kashimpur Central Jail on the outskirts of the capital.
"He was hanged at 10.35 PM (local time)," Home Minister Asaduzzaman Khan told PTI.
His execution came after 63-year-old Ali refused to seek presidential clemency on Friday.
The presidential mercy was the last resort for Ali, who was the infamous pro-Pakistan Al-Badr militia's third most important figure, to save his neck after the Supreme Court rejected his final review petition on Tuesday.
Earlier, authorities had called Ali's family to the prison to meet him.
"Twenty-two members of his family reached the jail to see him for the last time," private TV channels reported.
Ali, who owned several business houses and media outlets including a now suspended TV channel, was a central executive council member of Jamaat-e-Islami.
He pumped billions into the Jamaat since the mid-1980s to put it on a firm financial footing in Bangladesh.
He was convicted of running Al Badr's torture cell that carried out killings of several people.
Three million people were said to have been massacred in the war by the Pakistani army and their local collaborators.
Ali's hanging comes nearly four months after Jamaat-e-Islami chief Motiur Rahman Nizami was executed.
With the execution, Ali became the sixth top perpetrator to be hanged for the war crimes.
Before him, five war crimes convicts had been executed since Bangladesh initiated a trial process in 2010 for the 1971 war criminals. Of the five executed war crimes convicts, two had sought presidential clemency which was rejected.
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