High penetration of wind energy is pushing wind farms (WFs) to offer grid support capabilities, such as active power tracking. One of the main challenges in active power tracking for WFs is the interaction of wind turbines (WTs) through their wakes. This reduces the available wind in downstream WTs, leading them to saturation, while also affecting structural loading. With the increasing number of WTs in individual WFs, the computational and communication complexity of implementing centralized control architectures grows, posing challenges for real-world applications. In this article, we present a novel distributed control approach for active power tracking for WFs, namely multirate consensus-based distributed control (MCDC). The MCDC is designed to ensure that tracking errors caused by WT saturation are equally compensated throughout the WF, while only requiring local information exchanges between WTs. Furthermore, the proposed controller ensures that WT aerodynamic loading is balanced across the WF in a distributed manner. Finally, the overall power reference is distributed via a leader-follower consensus algorithm, resulting in a fully distributed approach. Our control approach facilitates the WF modularity and sparsity, which reduces the costs associated with control design and its applicability. Throughout this article, we demonstrate the effectiveness of the proposed MCDC through high-fidelity simulations, presenting performance comparable to the centralized control.