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, a systematic experimental study as a function of twist angle is still missing. Here we show that not only are moire excitons robust in bilayers of even large twist angles, but also properties of the moire excitons are dependant on, and controllable by, the moire reciprocal lattice period via twist-angle tuning. From the twist-angle dependence, we furthermore 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 heterostructures. Here, the authors show that the properties of the moire excitons in twisted van der Waals bilayers of transition metal dichalcogenides are determined by the moire reciprocal lattice period, and can be controlled via twist-angle tuning.