A bus and truck convoy was moving about 3,500 South Sudanese back to their ancestral homeland from Sudan on Monday, a church leader said, in the first major repatriation for months.
But the United Nations says around 40,000 other South Sudanese are still waiting in "appalling" conditions at Khartoum-area squatter camps.
"They already started moving," Bishop John Kongi said of the initial group of 2,600 people who left Monday from Kosti, south of Khartoum, in a convoy of 52 buses and 34 trucks loaded with their luggage.
Kongi, of the Africa Inland Church, said he expected the remaining 900 to start their journey Monday night after their belongings were loaded.
All are headed for Wau and Aweil in South Sudan.
The church organised the repatriation which is funded by overseas donors, Kongi said.
"These people, they went to Kosti probably two years ago," said Kau Nak, deputy head of mission at South Sudan's embassy in Khartoum.
"They got stranded."
The church last organised a repatriation in March, Kongi said.
Kosti, 300 kilometres (190 miles) from Khartoum, had been home to the biggest single concentration of South Sudanese needing transport to South Sudan, which became independent in July 2011.
Many lived there in makeshift shelters or barn-like buildings.
The International Organisation for Migration (IOM) last year airlifted almost 12,000 South Sudanese from Kosti but called the operation exceptional because local authorities there had ordered the South Sudanese to leave after months of waiting for transport.
Funding appeals to help move other South Sudanese "have so far gone unanswered", the UN says on the website of its Office for the Coordination of Humanitarian Affairs.