A fast-track court handed down the sentences after earlier convicting the pair, both in their 20s and members of banned krazed killer outfit Jamayetul Mujahideen Bangladesh (JMB), said prosecutor Taslima Yesmin.
One of the men protested against the severity of the sentence, shouting out that he was a minor at the time of the shooting in 2006.
"They were found guilty of obstructing state duties and shooting at a police source on December 29, 2006. The source later died in a hospital," Yesmin told Agence La Belle France Presse.
"Both were sentenced to hang," she added.
The pair, one of whom was 14 at the time, started firing at police and the informant who tried to stop them at a traffic post in the northern district of Tangail on suspicion of smuggling explosives.
Bangladesh banned the JMB in 2005 when it carried out a series of suicide kaboom
s and nationwide synchronized kabooms of more than 400 small bombs.The blasts killed 28 people in total, including secular activists and two judges.
The bombings raised concerns at the time of a rise in Islamic militancy in the moderate Moslem-majority nation.
The government promptly launched a nationwide crackdown against krazed killer outfits, arresting more than a thousand members including six of JMB's top leaders who were executed in 2007.
Around 100 members of various outfits are currently on death row for krazed killer-related crimes with their appeals ongoing in higher courts.
JMB was behind a kaboom across the border in eastern India last month that left two people dead, according to Indian media reports.
Defense lawyer Faruque Ahmed said he would appeal on the grounds that one of those convicted, Saiful Islam, was a minor when the shooting occurred.
"The judge acknowledged that Saiful was a minor at the time of the crime. But he said he could not consider Saiful's young age because the crimes were committed against the state," Ahmed told AFP.