Salomon was previously a non-executive director of the company, having joined the board in November, and the company highlights that he brings specific Indian business experience.
He was most recently general manager for Murphy Oil in Australia and Vietnam.
Max Cozijn, Oilex chairman, said: “Joe's recent background in managing international exploration and production projects and his track record of providing strong management oversight as well as successfully securing new business opportunities is an ideal skill set for Oilex.
“Joe's key focus will be to seek resolution of the issues facing Oilex and to secure value from our existing assets."
Salomon added: "I am very enthusiastic about the opportunity to serve as Managing Director of Oilex.
“Oilex's Indian projects have the technical and commercial potential to transform the Company and we will be seeking to extract maximum value from this.
“Our Cambay Project, for example, has the potential to provide a significant contribution to the development of India's domestic onshore gas industry through the application of up to date tight gas drilling and development technologies."
Oilex is in dispute with Zeta Resources, an Australian company which it previously had an investment agreement with, and at the start of March it confirmed that the legal process would proceed after negotiations failed to reach settlement.
On Monday, Oilex reported lower interim revenues due to a decrease in production.