In this paper, we present a whole-body Model Predictive Control framework for locomotion and validate it on the humanoid robot Talos. Using a time horizon of 1.5 second and a 20 Degree of Freedom model, the proposed controller outputs the optimal feedforward torque and Riccati-based feedback policy at a frequency of 100 Hz and the optimal feedback torque at 2 kHz. Contact constraints are handled through wrench regularization following a normal force reference in order to hint smooth force transitions to the solver. Contact locations and timings are user-defined, and Bezier curves are implemented as reference feet trajectories. Experimental validation includes dynamic locomotion at different gaits as well as 10 cm height stairstep crossing. To the best of the authors' knowledge, this experimental result marks the first achievement of locomotion on non-flat terrain for an electric torque-controlled humanoid robot using a full-dynamics Model Predictive Control scheme.