The development puts the army and its allies, including Lebanon's Hezbollah, within reach of Castelo Road, which rebels in Aleppo have relied on as a supply route leading to a countryside rear base.
An army spokesman told state television this "tightens the noose around the terrorists' positions in the eastern and northern edges of Aleppo, and cuts off the roads (they) were using to move from the northern countryside towards the city."
The regime refers to the rebels as "terrorists."
The advance into the area around the prison was preceded by an aerial assault Thursday, said the Observatory.
Rebel fighters have repeatedly attacked the prison since April 2013, hoping to free approximately 3,500 detainees, who are reportedly being held in dire conditions.
Troops inside the prison have fought to defend it.
The prison had nearly 4,000 inmates before the siege, including Islamists. Poor humanitarian conditions, including a lack of food and medicines, and the bombardment have caused the death of some 600 prisoners, according to the Observatory.
State television showed footage shot inside the prison, and a reporter interviewed both security forces and prisoners, including women.
The latest success comes on the heels of another significant victory for the regime, which this month reclaimed the Old City of Homs, Syria's third city once dubbed the "capital of the revolution."
The conflict flared when Assad's opponents took up arms in response to a bloody crackdown on a popular uprising in March 2011. It is estimated to have claimed at least 162,000 lives and displaced nearly half the population.
Despite the war, the Damascus regime is to stage a presidential election on June 3 in the areas under its control.
The exiled opposition has dismissed the election as a "farce," while the United States has branded it a "parody of democracy."
Assad, running for a third seven-year term against two virtual unknowns, is expected to stroll to victory in the poll.
In the eastern province of Deir Ezzor, 26 jihadists and rebels fighting the radical Islamic State of Iraq and the Levant (ISIL) were killed, as the extremist group pressed its advance on the Iraqi border and took over an oil rig in Al-Kharita, the Observatory said.
- Veto 'callous political move' -
Meanwhile, key Assad allies Russia and China vetoed a draft UN resolution that would have referred Syria to the International Criminal Court to examine chemical attacks, systematic torture, barrel bombings and blocked aid access.
This was the fourth time both countries have blocked Western resolutions relating to the conflict.
The 13 other members of the Security Council all voted in favour of the proposed resolution, which would have seen crimes committed by all sides in the country's war examined.
US Ambassador Samantha Power told the council that, as a result of the vetoes, "the Syrian people will not see justice today."
Amnesty International reacted by saying the vetoes are a "callous political move that betrays suffering people in Syria."
The world's chemical watchdog, meanwhile, said the last of Syria's chemicals agents are packed and ready to be taken to Latakia port and out of the country when the security situation permits.
"Some 100 metric tonnes of chemicals, or nearly 8 percent of Syria's declared stockpile, remain at a single site," Organisation for the Prohibition of Chemical Weapons chief Ahmet Uzumcu said.
"They have been packed and are ready for transportation (and) Syrian authorities have informed that they cannot yet be moved from the storage site due to the security situation in the area," an OPCW statement quoted him as saying.
Syria has already shipped out 92 percent of its stockpile from the Mediterranean port of Latakia.