We propose, implement and evaluate a natural human-machine control interface for a variable stiffness transradial hand prosthesis that achieves tele-impedance control through surface electromyography (sEMG) signals. This interface, together with variable stiffness actuation (VSA), enables an amputee to modulate the impedance of the prosthetic limb to properly match the requirements of a task, while performing activities of daily living. Both the desired position and stiffness references are estimated through sEMG signals and used to control the VSA hand prosthesis. In particular, regulation of hand impedance is managed through the impedance measurements of the intact upper arm; this control takes place naturally and automatically as the amputee interacts with the environment, while position of the hand prosthesis is regulated intentionally by the amputee through the estimated position of the shoulder. The proposed approach is advantageous, since the impedance regulation takes place naturally without requiring amputees' attention and diminishing their functional capability. Consequently, the proposed interface is easy to use, does not require long training periods or interferes with the control of intact body segments. The performance of the approach is evaluated through human subject experiments where adequate estimation of references and independent control of position and stiffness are demonstrated.