He was hanged at 10:01 PM local time, jail officials were quoted by local media reports as saying.
Quamaruzzaman, the third most influential leader in the Islamist party, was hanged late in the night after his execution was postponed at the last minute yesterday.
Quamaruzzaman, 63, is the second Jamaat leader after Quader Mollah to be executed for 1971 war crimes.
He had decided not to seek presidential clemency after the review of his conviction was rejected on April 6 by a four-member Supreme Court bench headed by Chief Justice Surendra Kumar Sinha.
More From This Section
He was found guilty of mass killing, murder, abduction, torture, rape, persecution and abetment of torture in central Mymensingh region. He was convicted for killing 164 people at a village in his home district in northern Sherpur.
The Supreme Court on November 3 last year upheld his death penalty. The apex court, however, issued the full text of the judgement on February 18 and sent it to the ICT, which immediately issued a death warrant.
The apex court called his crimes "worse than Nazis" when it upheld the judgement of the ICT.