Photonic brain-inspired platforms are emerging as novel analog computing devices, enabling fast and energy-efficient operations for machine learning. These artificial neural networks generally require tailored optical elements, such as integrated photonic circuits, engineered diffractive layers, nanophotonic materials, or time-delay schemes, which are challenging to train or stabilize. Here, we present a neuromorphic photonic scheme, i.e., the photonic extreme learning machine, which can be implemented simply by using an optical encoder and coherent wave propagation in free space. We realize the concept through spatial light modulation of a laser beam, with the far field acting as a feature mapping space. We experimentally demonstrate learning from data on various classification and regression tasks, achieving accuracies comparable with digital kernel machines and deep photonic networks. Our findings point out an optical machine learning device that is easy to train, energetically efficient, scalable, and fabrication-constraint free. The scheme can be generalized to a plethora of photonic systems, opening the route to real-time neuromorphic processing of optical data.