President Hamid rejected their mercy petitions soon after they sought presidential clemency in a last-ditch attempt to escape the gallows, a Bangabhaban spokesman told PTI.
"We have received the presidential decision...We are preparing to execute them any time in line with the jail code," a prison official told PTI.
Home Minister Asaduzzaman Khan said that preparations are underway to carry out the sentences.
"The Appellate Division (of the Supreme Court) had reconfirmed their death penalties more than 20 days ago and on receipt of the order and we immediately conveyed to them (the death row convicts)," the jail official said, suggesting that their execution was imminent.
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On March 19, the Supreme Court reconfirmed an earlier verdict of itself endorsing death penalty of Hannan and the two others for the 2004 attack on the then UK envoy.
The HuJI operatives carried out the attack at the shrine of saint Hazrat Shahjalal in Sylhet, also the birthplace of Chowdhury, as he went to visit there 18 days into his new assignment in Dhaka.
A speedy trial tribunal originally tried the case and delivered its verdict on December 23, 2008, sentencing to death HuJI leaders Sharif Shahedul Alam and Delwar Hossain alongside Hannan.
Hannan and seven other kingpins and operatives of Huji were earlier sentenced to death by another court in Dhaka for a deadly 2001 bomb attack that killed 10 people during Bengali New Year celebrations at a public park.
The then opposition leader Hasina narrowly escaped the attack that left 24 people dead.
HuJI was formed in 1992 by Bangladeshis who took part in the Afghan war against the Soviet forces in Afghanistan.
The US has designated HuJi as a foreign terrorist organization and "specially designated global terrorist" while Indian officials suspected the outfit's links in the Jaipur serial bombings and several other blasts there.