The use of magnetic resonance (MR) images for needle-based interventions offers several advantages over other types of imaging modalities (e.g., high tissue contrast and no radiation). However, MR-guided interventions face challenges related to electromagnetic compatibility of medical devices and real-time tracking of surgical instruments. This work presents a flexible needle steering system that combines an MR-compatible robot and a Fiber Bragg Grating (FBG)-based needle tip tracker. The MR images are used to localize obstacles and targets, while the FBG sensors provide strain measurements for online estimation of the needle tip position. A pre-operative planner defines the needle entry point and desired path, while a model predictive controller calculates the needle rotation during the insertion. To the best of the authors knowledge, this is the first work that fuses MR images and FBG-based tracking to steer a flexible needle in closed-loop inside the MR bore. The system is validated by steering a bevel-tipped flexible needle towards a physical target in gelatin phantoms and biological tissues. The needle reaches the target in all trials with an average targeting error of 2.76 mm. Disregarding the target displacement during the insertion, the average targeting error drops to 1.74 mm. The preliminary results demonstrate the feasibility of combining MR images and FBG-based needle tip tracking to steer a flexible needle in clinical procedures. In order to move towards to a clinically-relevant application, the design of a flexible Nitinol biopsy needle is also presented and evaluated by experiments in a prostate of a bull. The flexible needle presented a curvature 2.5 times larger than a conventional biopsy needle while maintaining the ability to collect tissue samples.