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 (\beta>\beta_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: (\beta,h) = (\beta_c,0).
