In this article, unlike the available literature, an optimal theorem is presented to design conditioning circuits for thermoelectric generator (TEG) energy harvesting without previous ad-hoc assumptions about the electric/electronic structure. The results show that simple linear time-invariant (LTI) conditioning circuits plus an extra non-linear element transforming the TEG's constant voltage into a square wave (ring oscillator) are in fact the optimal choice to pick up the biggest output's energy. This research opens the door to new developments: ring oscillators with ultra-low voltages (less than 1 mV) and nonlinear optimal control techniques applied to micro energy harvesting. Real measurement along with LT-Spice simulations is presented to validate the theoretical results, presenting transfer functions for simulation and modeling purposes.