The court, whose judgments cannot be appealed, ordered that Ahmad Shlash Hassan and Ezzo Hussein al-Hussein be hanged, their lawyer said on Thursday.
Two other defendants – Azzam al-Nahar and Abd al-Basset Hassida – were sentenced to forced labour for life while the rest of the accused received jail terms of between one and 20 years.
One of the two defendants sentenced to death was paraded on state television in May confessing to his involvement in the 27 April blast in Damascus.
Hassan, a 26-year-old veterinary student, said the bombing had been “a personal act”.
“I was trying to respond to the aggression against Muslims of oppressive states like Israel, the United States and all the other infidel countries,” he said.
The blast in late April in a vacant building formerly used by the United Nations in Damascus’s Mazzeh diplomatic district sparked a firefight with security forces in which two armed men, a police officer and a female passer-by were killed.
A previously unknown group claimed respsonsibility, but some US lawmakers suggested the attack was staged by the Syrian intelligence services, a charge vigorously denied by Damascus.
The Martyr Adib al-Kilani Group said the attack was to avenge the victims of the 1982 bombing of the northern town of Hama to quell the Muslim Brotherhood.
“I was trying to respond to the aggression against Muslims of oppressive states like Israel, the United States and all the other infidel countries”
A vacant basement of the targeted building belonged to Rifaat al-Assad, an exiled uncle of Syrian President Bashar al-Assad who was in charge of security forces in 1982.
Most political parties have been banned in Syria since 1958.
After the Baath party came to power in a coup in 1963, the Muslim Brotherhood continued to function underground, but its members were subject to arrest and imprisonment.
From the late 1970s the Muslim Brotherhood was involved in armed clashes with government forces, and in July 1980 membership of the organisation was made punishable by death.
In the 1980s, many Syrian Muslim Brotherhood detainees were extrajudicially executed in custody, according to rights group Amnesty International.