In this paper, we determine the degree distance of $G\times K_{r_0,r_1,\ldots,r_{n-1}}$ and $G\boxtimes K_{r_0,r_1,\ldots,r_{n-1}}$, where $\times$ and $\boxtimes$ denote the tensor product and strong product of graphs, respectively, and $K_{r_0,r_1,\ldots,r_{n-1}}$ denotes the complete multipartite graph with partite sets $V_0,V_1,\ldots,V_{n-1}$ where $|V_j|=r_j$, $0\leq j\leq n-1$ and $n\geq 3$. Using the formulae obtained here, we have obtained the exact value of the degree distance of some classes of graphs.