Exact closed form expressions are derived for the photon number distribution functions and the factorial moments in resonance fluorescence from a two-level atom that is driven on or near resonance by a laser beam of finite bandwidth. Derivation procedure that was used by Lenstra in the theory of photon number statistics for limited cases is applied to our generalized problem with help of the theory of resonance fluorescence with excitation of finite bandwidth. All of the results are presented in a fully suitable form for practical analyses of statistical features of resonance fluorescence.