Franklin is presently interim chair at Statoil, he will be deputy chair and senior independent director at post-merger Amec Foster Wheeler / Wood Group and he is on the advisory board of private equity investment group Kerogen Capital.
He joins Premier Oil with effect from September 1.
"I very much look forward to joining the board and chairing Premier, a company I have known well for many years,” Franklin said in a statement.
“I would like to congratulate Mike Welton on leading the company through a very challenging industry downturn and very much look forward to working with the Board, the management team and all stakeholders.”
Outgoing chairman Mike Welton in March announced his intention to leave the position.
Welton added: “It has been a privilege to have been Chairman of Premier for some eight years. It is a company with great potential and I am sure that Roy is an excellent choice to chair the Board for the next phase of its development."
Additionally, the oil firm is hiring Dave Blackwood and Mike Wheeler to the board as non-executive directors with immediate effect.