Measurement While Drilling (MWD) is a technology for assessing rock mass conditions by collecting and analyzing data of mechanical drilling variables while the system operates. Nowadays, typical MWD systems rely on physical sensors directly installed on the drill rig. Sensors used in this context must be designed and conditioned for operating in harsh conditions, imposing trade-offs between the complexity, cost, and reliability of the measurement system. This paper presents a methodology for integrating physics-based observers into an MWD system as an alternative to complement or replace traditional physical sensors. The proposed observers leverage mathematical models of the drill’s electrical motor and its interaction with dynamic loads to estimate the bit speed and torque in a Down-the-Hole rig using current and voltage measurements taken from the motor power line. Experiments using data collected from four test samples with different rock strengths show a consistent correlation between the rate of penetration and specific energy derived from the observed drilling variables with the ones obtained from standardized tests of uniaxial compressive strength. The simplicity of the setup and results validate the feasibility of the proposed approach to be evaluated as an alternative to reduce the complexity and increase the reliability of MWD systems.