In this paper, a novel motion learning method is introduced: Fast Marching Learning (FML). While other learning methods are focused on optimising probabilistic functions or fitting dynamical systems, the proposed method consists on the modification of the Fast Marching Square (FM2) path planning algorithm. Concretely, FM2 consists of expanding a wave through the environment with a velocity directly proportional to the distance to the closest obstacle. FML modifies these velocities in order to generalise the taught motions and reproduce them. The result is a deterministic, asymptotically globally stable learning method free of spurious attractors and unpredictable behaviours. Along the paper, detailed analysis of the method, its properties and parameters are carried out. Comparison against a state-of-the-art method and experiments with real data is also included.