The bombings blew away the front of a nine-story intelligence headquarters, leaving a gruesome scene of burned bodies and burning vehicles along the highway in front of the building, The New York Times reported.
Military personnel and civilians were among the 55 dead and 372 people injured. A source at a military hospital said at least 11 soldiers were killed.
The Syrian Health Ministry said 15 dead were unidentified remains.
The explosions occurred during the morning rush hour as government employees went to work and children went to school.
A statement from the Interior Ministry read on state-run television said two suicide car bombs carrying more than 2,200 pounds of explosives were detonated, destroying 21 vehicles and damaging more than 100 others.
The compound was home to two major branches of the military intelligence, one known officially as the Palestine Branch that held hundreds of prisoners and the other known as the Patrols Branch, which maintained and dispatched intelligence vehicles that patrolled the Damascus area.
The attack was the biggest and deadliest reported since the uprising began in March 2011.
Maj. Gen. Robert Mood, the Norwegian officer leading the United Nations observer mission that is monitoring the fragile, month-old cease-fire, visited the scene soon after the blast.
"This is yet another example of the suffering brought upon the people of Syria from acts of violence," Mood said in a statement aired on state television. "We, the world community, are here with the Syrian people, and I call on everyone within and outside Syria to help stop this violence."
There was no immediate claim of responsibility although each side blamed the other. The official media said it was the work of "terrorists" while opposition groups blamed President Bashar Assad's regime.
The blasts occurred just hours after a leading opposition activist group said government forces have killed hundreds since the cease-fire brokered by U.N.-Arab League envoy Kofi Annan went into effect April 12, CNN said.
As of Wednesday, at least 1,025 people have been killed, the Local Coordination Committees of Syria said.
U.N. leaders had said Syria risked devolving into a civil war if the cease-fire isn't honored.
"If this opportunity is not seized, I fear that what joint special envoy Kofi Annan has warned about will come to pass: a full-scale civil war with catastrophic effects within Syria and across the region," U.N. Secretary-General Ban Ki-moon said.
The violence has continued despite the U.N.-backed peace plan Ban said is the only chance to stabilize the country.
"There is no escaping the reality that we see every day: innocent civilians dying, government troops and heavy armor in city streets, growing numbers of arrests and allegations of brutal torture," he said.
Opposition members and world leaders have accused Assad of failing to observe the truce despite his pledge to do so, saying attacks have occurred almost daily, including gunfire from security forces that killed three people in Daraa, Homs and Idlib provinces Thursday.