The first 500 members of the LRA arrived at the Ri-Kwangba camp in southern Sudan, 500m north of the border with the Democratic Republic of Congo (DRC), on Sunday.
They were led by Vincent Otti, the mainly Ugandan group's deputy commander, Riek Machar, south Sudan's vice-president, said on Sunday.
Machar said: "They have shown up in the western assembly point in Ri-Kwangba. They have also shown up in Owiny-ki-Bul."
Machar said that Joseph Kony, the LRA's leader, was following behind Otti with more of his soldiers and was also making his way to Ri-Kwangba camp.
The LRA has agreed to assemble in the camps as the first part of a peace deal signed three weeks ago.
The deal says that rebel fighters gathering in the camp will be protected while a broader peace deal is negotiated.
The rebels have walked to both sites from their hideouts in the DRC since the truce was signed last month.
Machar is mediating the ongoing peace talks between the rebels and the Ugandan government.
A key part of the deal will be working out what will happen to several LRA commanders, including Kony, who are wanted by the Hague-based international criminal court.
The rebels have been told that while in the camps they will also be protected from efforts to put them on trial or extradite them to Brussels.
Ugandan fighters are travelling from Congo into southern Sudan
News of the rebels' arrival in the camps came as Jan Egeland, the UN humanitarian chief, who is in Juba to hold talks with both sides, promised that the UN would provide support at the two sites where the rebel fighters are gathering.
"We hope the peace talks will lead to a durable peaceful solution and we will do our utmost in helping that," Egeland told reporters after meeting with Machar.
Egeland also said the UN would step in to help women and children who are released by the Lord's Resistance Army.
Earlier on Monday, the rebels said they were willing to release women and children who have been seized during the conflict.