This research paper sought to characterize the boundedness and compactness of composition operators from the space ${\mathcal{H}}^{\mathrm{\infty }}$ of bounded harmonic mappings into harmonic Zygmund space ${\mathcal{Z}}_H$, on the open unit disk. Furthermore, we obtain an estimate of the essential norms of such an operator. These results extends the similar results that were proven for composition operators on analytic function spaces.