Moire lattices formed in twisted van der Waals bilayers provide a unique, tunable platform to realize coupled electron or exciton lattices unavailable before. While twist angle between the bilayer has been shown to be a critical parameter in engineering the moire potential and enabling novel phenomena in electronic moire systems, studies of moire excitons so far have focused on closely angularly-aligned heterobilayers. The twist-angle degree of freedom has been largely considered detrimental to the observation of moire excitons. Here we report robust moire excitons in bilayers of even large twist angles formed due to Umklapp scattering by the moire reciprocal lattice vectors, and we furthermore demonstrate twist-angle tuning of the properties of the moire excitons as a result of varying moire reciprocal lattice periods. We develop an intuitive analytical model to explain our results, and, from the twist-angle dependence, obtain the effective mass of the interlayer excitons and the electron inter-layer tunneling strength, which are difficult to measure experimentally otherwise. These findings pave the way for understanding and engineering rich moire -lattice induced phenomena in angle-twisted semiconductor van der Waals semiconductor heterostructures.