Carrying backpacks and suitcases and accompanied by their teachers, the students walked three kilometres (two miles) Thursday from Yarmuk to rebel-held Yalda, which has been calm since a 2014 ceasefire.
"I'm happy I'll take my exams, but I'll also be able to see my family outside Yarmuk who I haven't seen in a long time," said Fadi.
The students were driven from Yalda into Damascus, where on Sunday they will sit national curriculum examinations.
A young Palestinian girl waiting to begin the trek told AFP she was scared.
"I don't want to leave my mother in the camp, but I have to go because I can't take the test here," she said.
Teachers had petitioned a Palestinian official in Damascus to allow students to take their exams there, as those administered in the camp are not recognised by the state, an AFP correspondent in Yarmuk said.
Walid al-Kurdi received government permission and then negotiated with Al-Qaeda's Syrian affiliate, which controls swathes of the camp along with other rebel groups.
All roads out of Yarmuk are shut or regime-controlled.
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Chris Gunness, spokesman for the UN's Palestinian refugee agency, said 155 Palestinian students had left Yarmuk with the help of the authorities, and were receiving food and other aid from UNRWA.
It is the second time Yarmuk students have been granted special permission to take exams in Damascus.
The camp was once a vibrant home to some 160,000 people, but has been ravaged by a devastating government siege, bombing and clashes.
Last month, much of the camp was overrun by the Islamic State group, though its fighters have since been pushed back to Yarmuk's southwest.
On Friday, UNRWA published a photo of Amira, a two-month old child born just before the fighting with IS began, calling it "an image that should shame the world".
The tiny child, wrapped in blankets, weighs just one kilo. Her mother calls her "a baby of the siege".
"UNRWA has demanded and continues to demand humanitarian access to civilians in Yarmuk, people like Amira and her family who are living life on the very edge of existence," Gunness wrote in a statement.
"This has become a test of the international system. We must not fail."