The decision was reached during the two-day official visit of President Goodluck Jonathan to Namibia at the invitation of his counterpart, President Hifikepunye Pohamba.
This is contained in a joint communiqué issued on the visit and made available to the News Agency of Nigeria (NAN) in Windhoek, Namibia.
It stated that the refinery, which would be located in Walvis Bay, would be wholly private financed.
The two leaders urged the private sector of both countries to work toward a speedy realisation of the joint oil refinery.
They commended the hosting of a business forum between the private sector stakeholders of both countries on the margin of the state visit.
The leaders urged their respective private sector stakeholders to take the full advantage of the abundant business opportunities, to optimise trade and commerce between the two countries.
Meanwhile, the Federal Government has agreed to train Namibian diplomats at the Nigerian Foreign Service Academy.
The Federal Government also agreed to provide volunteer health professionals to Namibia under the Technical Aid Corps, TAC, Scheme.
The agreements were among the 11 Memoranda of Understanding, MoU, signed by both countries to broaden and deepen bilateral cooperation.
Others are: Agreement on Youth Development, Bilateral Air Service Agreement and Agreement on Waiver of visa requirements for citizens holding diplomatic and official passports and Extradition Treaty.
They also sign Cooperation in the legal field, Treaty on Mutual Legal Assistance in Criminal Matters and in the Field of Geology, Mining, Mineral Processing and Metallurgy.
The others are Trade, Investment and Economic Cooperation and on Cooperation in the Field of Tourism.