Soft robotics have broken the rigid wall of interaction between humans and robots due to their own definition and manufacturing principles, allowing robotic systems to adapt to humans and enhance or restore their capabilities. In this research we propose a dexterous bioinspired soft active hand prosthesis based in the skeletal architecture of the human hand. The design includes the imitation of the musculoskeletal components and morphology of the human hand, allowing the prosthesis to emulate the biomechanical properties of the hand, which results in better grips and a natural design. CAD models for each of the bones were developed and 3D printing was used to manufacture the skeletal structure of the prosthesis, also soft materials were used for the musculoskeletal components. A myoelectric control system was developed using a recurrent neural network (RNN) to classify the hand gestures using electromyography signals; the RNN model achieved an accuracy of 87% during real time testing. Objects with different size, texture and shape were tested to validate the grasping performance of the prosthesis, showing good adaptability, soft grasping and mechanical compliance to object of the daily life.