The financial details were not disclosed, but Statoil said it will retain a 40 percent stake in the licence, which concerns two blocks in the Rovuma basin and for which it will remain the operator.
In addition to Statoil and Inpex, the partners in the licence are Britain's Tullow, with 25 percent, and the Mozambican state-owned company Empresa Nacional de Hidrocarbonetos, with 10 percent.
The licence covers more than 8,000 square kilometres (3,088 square miles) in waters where the depth varies from 300 to 2,500 metres (980 to 8,200 feet).
"Large gas discoveries have recently been made north of the acreage and the prospectivity for hydrocarbons in the Statoil-operated blocks is promising," a Statoil senior vice president, Nick Maden, said in a statement.
The southeast African country has become an important player in the global energy market, home to more than 40 percent of gas discoveries made worldwide last year.
The first of two exploratory wells will be drilled in the second quarter, Statoil said.
The sale to Inpex requires the approval of the Mozambican government.