In this paper, we propose a harmonic-model based control approach for the three-phase grid-tied AC-DC converter. We derive a nonlinear harmonic domain model and demonstrate its efficacy in designing harmonic control with global stability guarantees. Furthermore, we establish that this harmonic control design can be translated into a periodic nonlinear control scheme in the time domain, maintaining the same level of stability guarantees. Additionally, the proposed framework allows to incorporate control objectives specifically related to harmonic distortion and harmonic mitigation as well as the tracking of periodic trajectories. Illustrative simulations and experimental setups were conducted to evaluate the effectiveness of the proposed methodology in reducing Total Harmonic Distortion (THD) in real-time. The obtained results demonstrate the successful achievement of the desired control objectives, validating the efficacy of the proposed harmonic control approach.