An army statement said the evacuees numbered 38 children and 25 women.
It says two children were transported to hospital and it appealed to the militants still inside the battered camp to surrender and face a fair trial.
A spokeswoman for the International Committee of the Red Cross (ICRC) says among the group were two children and three women injured in an explosion inside the Nahr al-Bared camp.
The military agreed to a temporary truce with the Fatah al-Islam fighters to allow the last civilians to leave the camp, which has been mostly reduced to rubble following more than three months of intense shelling and air raids by the army.
Three military buses filled with women veiled in black from head to toe and children were seen leaving the camp followed by several ambulances.
They were taken under heavy security to a nearby military base for questioning.
Sheikh Mohammed Hajj, spokesman for a group of Palestinian clerics involved in mediations, says the evacuees included the widow and child of Abu Hureira, Fatah al-Islam's number two, who was killed recently, and the wife of the group's chief, Shaker al-Abssi.
He says the women included 12 Syrians or Syrian-Palestinians, and that the rest were Lebanese.
"The women and children were allowed to shower and were fed on their arrival at the military base and were treated well by female officers," Mr Hajj says.
‘Fight to the death’
The evacuation could pave the way for the army to launch a final assault on the Al-Qaeda-inspired militants, who have refused demands to surrender and vowed to fight to the death.
Immediately following the evacuation in late afternoon, the army resumed its shelling of Fatah al-Islam positions.
"The militants have decided to fight all the way so there will be fierce battles," Elias Hanna, a retired army general and military analyst, says.
“The army will say that the end is near so they have to go into the last corner to kill or capture Fatah al-Islam."
Mr Hajj says his group had reestablished contact with a spokesman for the Islamists after losing touch for three days.
"Abu Salim Taha contacted us again and said that the civilians are ready to leave the camp," he says.
Negotiations to evacuate the families began overnight Monday after Taha called the clerics seeking a way out for the civilians who have been inside the camp since May 20, when the clashes erupted.
The militants, thought to number about 70, have been besieged for the past two months in a small area in the southern part of the camp, hiding in well-equipped underground shelters, according to the army.
The advance of troops has been hampered because of the camp's winding streets and the booby traps and mines left by the militants.
At least 200 people, including 142 soldiers, have been killed in the fighting, the deadliest internal unrest in Lebanon since the 1975-1990 civil war.