We propose a variable stiffness prosthetic hand and present its surface electromyography (sEMG) interface for tele-impedance control. Such an interface, together with variable stiffness actuation (VSA), enables the amputee to modulate the impedance of the prosthetic limb to properly match the requirements of the task at hand, while performing activities of daily living. Both the desired position and stiffness of the hand are estimated through sEMG signals and these estimates are employed to control the VSA hand prosthesis. In particular, regulation of finger impedance is managed through the impedance measurements of the intact forearm; 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 thumb, extracted from sEMG signals of the dysfunctional agonistic and antagonistic thumb muscles that are embedded in the forearm. The proposed approach is advantageous, since the impedance regulation takes place naturally from task to task or during execution of a single task without requiring amputees' attention and diminishing their functional capability. Consequently, the proposed interface does not require long training periods or interfere with control of intact body segments, and provides amputee with easiness in use. The performance of the tele-impedance control of the VSA hand prosthesis is experimentally evaluated. Experimental results indicate that both position and stiffness can be adequately estimated using sEMG signals and regulated through VSA.