Dhaka Central Jail Superintendent Jahangir Kabir confirmed that the two were executed at the same time at 12:55am on Sunday.
With Sunday’s execution, Bangladesh has hanged four war crimes convicts so far.
Jamaat leader Abdul Quader Molla was the first to walk the gallows in December 2013 while another leader of the same party Mohammad Kamaruzzaman was executed in April this year.
Chowdhury, 67, and Mujahid, 68, were executed after their petitions for presidential clemency was turned down earlier on Saturday.
On Wednesday, the Supreme Court scrapped their petitions for a review of their death sentences.
Copies of the verdicts were published and sent to the jail on Thursday. The same day, the prison authorities read the verdicts out to the convicted war criminals.
The only hurdle for the executions was a possible presidential clemency, which they had sought on Saturday, but in the end, that plea was turned down.
Former BNP MP Salauddin Quader, who had also served as a minister during HM Ershad’s regime, was sentenced to death by the International Crimes Tribunal (ICT) on Oct 1, 2013.
The verdict depicted how he had led the Pakistani army to murder and loot in 1971, and how he had abducted freedom fighters and pro-liberation people, taking them to his hilltop residence in Chittagong and torturing them.
Mujahid, a minister in Khaleda Zia’s coalition Cabinet, planned and executed mass murders including those of intellectuals, scientists, academics and journalists in 1971.
On Jul 17, 2013, the ICT gave him the death sentence after he was proven guilty of mass killings and torture of Hindus during the Liberation War.
Both of them appealed against the verdicts, but the Supreme Court upheld their death sentences.
Chief Justice Surendra Kumar Sinha headed the four-member Appellate Division bench that, on June 16, gave its verdict on Mujahid, who was the former commander of Al-Badr, the militia raised by Pakistan to crush the Bengali struggle for independence.
The same bench delivered the verdict on Chowdhury’s appeal against capital punishment on Jul 29.
The two full verdicts were published on Sep 30.
The ICT issued the death warrants the next day and sent them to the prison. The warrants were read out to the convicts.
Both convicts then filed a petition for a review of their death sentences, which was rejected by the Chief Justice led appeals bench.
[Additional reporting by Liton Haider, Sumon Mahbub, Kamal Talukder, Sajidul Haque, Golam Mujtaba Dhruba, Ashik Hossain, Nayan Kumar, Tanvir Ahmed]