In March, the African neighbours agreed to resume cross-border oil flows.
Landlocked South Sudan had shut down its production of up to 350,000 barrels per day (bpd) in January 2012 after failing to agree with Sudan over oil fees. The new nation, which seceded from Sudan in 2011, needs to export its oil through Sudan.
The first oil from the Palouge field in South Sudan's Upper Nile state will be sent to Sudan on May 10, oil ministry undersecretary Awad Abdel-Fattah told SUNA after a phone call with the head of oil consortium Dar Petroleum which runs the fields.
In the coming days, South Sudan plans to reopen its fields in Upper Nile state, which produce Dar Blend, a heavy, sour crude.
Last month, South Sudan started resuming oil production in Unity state but damage caused by cross-border skirmishes a year ago means the output is only gradually rising. The fields produce Nile Blend, a light, sweet, waxy crude.
Industry experts say Dar Blend production will start at around 50,000 bpd, and quickly rise to at least 150,000 bpd, while Nile Blend is likely to remain at around 30,000-40,000 bpd for at least six months.
Both countries, which came close to returning to war a year ago, depend heavily on crude exports for state revenues and use the foreign currency to import food and fuel.
South Sudan seceded from Sudan in 2011 under a 2005 peace deal which ended one of Africa's longest civil wars. However, the two remain at loggerheads over control of disputed territories and other issues.