In this paper we define the tensor product of two A∞-categories and two A∞- functors. This tensor product makes the category of A∞-categories symmetric monoidal (up to homotopy), and the category A∞Catu/≈ a closed symmetric monoidal category. Moreover, we define the derived tensor product making Ho(A∞Cat), the homotopy category of the A∞-categories, a closed symmetric monoidal category. We also provide an explicit description of the internal homs in terms of A∞-functors.