We derive a precise Ornstein-Zernike asymptotic formula for the decay of the two-point function 〈s_0 s_x〉_β in the general context of finite range Ising type models on ℤ^d. The proof relies in an essential way on the a-priori knowledge of the strict exponential decay of the two-point function and, by the sharp characterization of phase transition due to Aizenman, Barsky and Fernández, goes through in the whole of the high temperature region β<βc. As a byproduct we obtain that for every β<βc, the inverse correlation length ξ_β is an analytic and strictly convex function of direction.