This paper presents an adaptive impedance control architecture for robotic teleoperation of contact tasks featuring continuous interaction with the environment. We use Learning from Demonstration (LfD) as a framework to learn variable stiffness control policies. Then, the learnt state-varying stiffness is used to command the remote manipulator, so as to adapt its interaction with the environment based on the sensed forces. Our system only relies on the on-board torque sensors of a commercial robotic manipulator and it does not require any additional hardware or user input for the estimation of the required stiffness. We also provide a passivity analysis of our system, where the concept of energy tanks is used to guarantee a stable behavior. Finally, the system is evaluated in a representative teleoperated cutting application. Results show that the proposed variablestiffness approach outperforms two standard constant-stiffness approaches in terms of safety and robot tracking performance.