The controllable growth of two-dimensional (2D) heterostructure arrays is critical for exploring exotic physics and developing novel devices, yet it remains a substantial synthetic challenge. Here we report a rational synthetic strategy to fabricate mosaic heterostructure arrays in monolayer 2D atomic crystals. By using a laser-patterning and an anisotropic thermal etching process, we create periodic triangular hole arrays in 2D crystals with precisely controlled size and atomically clean edges, which function as robust templates for endoepitaxial growth of another 2D crystal, to obtain monolayer mosaic heterostructures with atomically sharp heterojunction interfaces. Systematic microstructure and spectroscopic characterizations reveal periodic modulation of chemical compositions, lattice strains and electronic band gaps throughout the mosaic heterostructures. The robust growth of the monolayer mosaic heterostructures with a high level of synthetic control opens a pathway for band structure engineering and spatially modulating the potential landscapes in the atomically thin 2D crystals, establishing a designable material platform for fundamental studies and development of complex devices and integrated circuits from 2D heterostructures.