The truncated two-point function of the ferromagnetic Ising model on $\mathbb Z^d$ ($d\ge3$) in its pure phases is proven to decay exponentially fast throughout the ordered regime ($β>β_c$ and $h=0$). Together with the previously known results, this implies that the exponential clustering property holds throughout the model's phase diagram except for the critical point: $(β,h) = (β_c,0)$.