Nanophotonics, the field that merges photonics and nanotechnology, has in recent years revolutionized the field of optics by enabling the manipulation of light-matter interactions with subwavelength structures. However, despite the many advances in this field, the design, fabrication and characterization has remained widely an iterative process in which the designer guesses a structure and solves the Maxwell's equations for it. In contrast, the inverse problem, i.e., obtaining a geometry for a desired electromagnetic response, remains a challenging and time-consuming task within the boundaries of very specific assumptions. Here, we experimentally demonstrate that a novel Deep Neural Network trained with thousands of synthetic experiments is not only able to retrieve subwavelength dimensions from solely far-field measurements but is also capable of directly addressing the inverse problem. Our approach allows the rapid design and characterization of metasurface-based optical elements as well as optimal nanostructures for targeted chemicals and biomolecules, which are critical for sensing, imaging and integrated spectroscopy applications.