Concentric tube robots are continuum robots particularly well-suited for minimally-invasive surgery. Their small diameter, natural free channel and snake-like shape unlock the potential for applications that require a high degree of dexterity in confined spaces. The synthesis and planning of such robots are generally based on the patient’s anatomy and the type of surgery to be performed. However, their practical deployment can be challenging. Open-loop approaches are prone to errors due to modeling accuracy or physiological motions of the patient during the procedure, and human-in-the-loop approaches require specific skills from the surgeon. In this article, we propose an automatic tip-steering approach for concentric tube robots based on visual SLAM (simultaneous localization and mapping). This allows a closed-loop control scheme to compensate for open-loop errors, and provides to the surgeon the opportunity to focus on the medical procedure, simplifying the management of the deployment. A method is proposed in the case of a robot geometry that achieves approximate follow-the-leader deployment. It is validated by performing an automatic tip-steering task in the trachea using a realistic simulator for concentric tube robots.