She is currently interim chief executive at Liverpool’s Everyman and Playhouse Theatres and was formerly business director of Bolton’s Octagon Theatre.
Gibson will begin the role at Capital Theatres on April 20, 2020, following the retirement of current chief executive Duncan Hendry.
Chair of the board of Capital Theatres Joan Stringer said: “Fiona brings an exceptional skill set and a broad range of experience, working across a number of sectors, arts and business.
“As we look to the start of our £25 million redevelopment of the King’s Theatre, with building works commencing in 2021, Fiona will provide inspirational leadership to continue the success of Capital Theatres into its next exciting era.”
Gibson added: “What an amazing time to be joining this wonderful, world-renowned institution.
“Capital Theatres sits at the heart of culture in Scotland and I am privileged to be taking over the reins at such an exciting period of change.”