The approximate 70,000 sq km area is adjacent to Petronas' Gambela Block in the north and borders South Sudan and Kenya to the south.
The Agreement is over a two-year period during which White Nile, in collaboration with the Petroleum Operations Department of the Ministry of Mines, will conduct geological and geophysical studies aimed at evaluating the prospective nature of the area for oil.
At the conclusion of the Agreement period or at any time before that, the terms allow the Company to enter exclusive negotiations with the Ministry of Mines for an Exploration and Production Sharing Agreement.
Exploration in the area is based on the geological concept that the petroliferous Cretaceous and Early Tertiary basins of South Sudan extend south-eastwards beneath the younger and less prospective East African rifts.
The Company, which has an initial cash commitment of $450,000 plans to begin geophysical operations in September with magneto-telluric and gravity surveys.
White Nile has recently commissioned an extensive seismic survey on its Block Ba exploration concession in South Sudan.
The Company is aiming to build a strong regional presence focussing on oil exploration and production.
White Nile Chairman Phil Edmonds said: "We are very pleased that we have agreed terms with the Ethiopian Government and hope this is the start of a long running relationship."
"We will work closely with the Ministry of Mines to evaluate the area, which both parties believe has strong potential for future development, especially due to it being adjacent to the highly prospective Gambela region.
"Following the conclusion of the exploration work programme and the analysis of the data collected, we aim to progress the project in tandem with the Ethiopian Government to maximise the potential of the region as quickly as possible.
"We have recently raised an additional GBP7 million from institutions and have engaged Canadian company Terra Seis Geophysical Ltd to conduct an initial 2,000km seismic survey on the Block Ba concession area in South Sudan.
"We are also continuing to work closely with our partners and advisors to identify further concession areas in Southern Sudan and adjacent countries, which will fulfil the Company's strategy of creating a strong presence within the region and help in the enhancement of its oil potential," Edmonds said in a statement.