While minimally invasive surgery offers great benefits in terms of reduced patient trauma, bleeding, as well as faster recovery time, it still presents surgeons with major ergonomic challenges. Laparoscopic surgery requires the surgeon to bimanually control surgical instruments during the operation. A dedicated assistant is thus required to manoeuvre the camera, which is often difficult to synchronise with the surgeon’s movements. This article introduces a robotic system in which a rigid endoscope held by a robotic arm is controlled via the surgeon’s eye movement, thus forgoing the need for a camera assistant. Gaze gestures detected via a series of eye movements are used to convey the surgeon’s intention to initiate gaze contingent camera control. Hidden Markov Models (HMMs) are used for real-time gaze gesture recognition, allowing the robotic camera to pan, tilt, and zoom, whilst immune to aberrant or unintentional eye movements. A novel online calibration method for the gaze tracker is proposed, which overcomes calibration drift and simplifies its clinical application. This robotic system has been validated by comprehensive user trials and a detailed analysis performed on usability metrics to assess the performance of the system. The results demonstrate that the surgeons can perform their tasks quicker and more efficiently when compared to the use of a camera assistant or foot switches.