Purpose To develop a rapid and accurate MRI phase‐unwrapping technique for challenging phase topographies encountered at high magnetic fields, around metal implants, or postoperative cavities, which is sufficiently fast to be applied to large‐group studies including Quantitative Susceptibility Mapping and functional MRI (with phase‐based distortion correction). Methods The proposed path‐following phase‐unwrapping algorithm, ROMEO, estimates the coherence of the signal both in space—using MRI magnitude and phase information—and over time, assuming approximately linear temporal phase evolution. This information is combined to form a quality map that guides the unwrapping along a 3D path through the object using a computationally efficient minimum spanning tree algorithm. ROMEO was tested against the two most commonly used exact phase‐unwrapping methods, PRELUDE and BEST PATH, in simulated topographies and at several field strengths: in 3T and 7T in vivo human head images and 9.4T ex vivo rat head images. Results ROMEO was more reliable than PRELUDE and BEST PATH, yielding unwrapping results with excellent temporal stability for multi‐echo or multi‐time‐point data. It does not require image masking and delivers results within seconds, even in large, highly wrapped multi‐echo data sets (eg, 9 seconds for a 7T head data set with 31 echoes and a 208 × 208 × 96 matrix size). Conclusion Overall, ROMEO was both faster and more accurate than PRELUDE and BEST PATH, delivering exact results within seconds, which is well below typical image acquisition times, enabling potential on‐console application.