Hand loss is a highly disabling event that markedly affects the quality of life. To achieve a close to natural replacement for the lost hand, the user should be provided with the rich sensations that we naturally perceive when grasping or manipulating an object. Ideal bidirectional hand prostheses should involve both a reliable decoding of the user's intentions and the delivery of nearly "natural" sensory feedback through remnant afferent pathways, simultaneously and in real time. However, current hand prostheses fail to achieve these requirements, particularly because they lack any sensory feedback. We show that by stimulating the median and ulnar nerve fascicles using transversal multichannel intrafascicular electrodes, according to the information provided by the artificial sensors from a hand prosthesis, physiologically appropriate (near-natural) sensory information can be provided to an amputee during the real-time decoding of different grasping tasks to control a dexterous hand prosthesis. This feedback enabled the participant to effectively modulate the grasping force of the prosthesis with no visual or auditory feedback. Three different force levels were distinguished and consistently used by the subject. The results also demonstrate that a high complexity of perception can be obtained, allowing the subject to identify the stiffness and shape of three different objects by exploiting different characteristics of the elicited sensations. This approach could improve the efficacy and "life-like" quality of hand prostheses, resulting in a keystone strategy for the near-natural replacement of missing hands.