The project has been approved by the Board of Investment, the investment promotion agency that grants investors tax and other concessions.
Yapa has previously said the planned refinery's entire output will be shipped to overseas markets.
The refinery project will provide employment to about 700 people in the area, one of Sri Lanka's most neglected districts where unemployment and poverty are high.
It is the home electorate of Sri Lanka's president Mahinda Rajapakse.
The government has also started work with Chinese funds to build a new port in Hambantota, to exploit its location close to the main shipping lane across the Indian Ocean.
The new refinery investment comes at a time when Sri Lanka is offering petroleum firms the chance to bid for oil exploration blocks in