The integration of various two-dimensional (2D) materials on wafers enables a more-than-Moore approach for enriching the functionalities of devices1-3. On the other hand, the additive growth of 2D materials to form heterostructures allows construction of materials with unconventional properties. Both may be achieved by materials transfer, but often suffer from mechanical damage or chemical contamination during the transfer. The direct growth of high-quality 2D materials generally requires high temperatures, hampering the additive growth or monolithic incorporation of different 2D materials. Here we report a general approach of growing crystalline 2D layers and their heterostructures at a temperature below 400 °C. Metal iodide (MI, where M = In, Cd, Cu, Co, Fe, Pb, Sn and Bi) layers are epitaxially grown on mica, MoS2 or WS2 at a low temperature, and the subsequent low-barrier-energy substitution of iodine with chalcogens enables the conversion to at least 17 different 2D crystalline metal chalcogenides. As an example, the 2D In2S3 grown on MoS2 at 280 °C exhibits high photoresponsivity comparable with that of the materials grown by conventional high-temperature vapour deposition (~700-1,000 °C). Multiple 2D materials have also been sequentially grown on the same wafer, showing a promising solution for the monolithic integration of different high-quality 2D materials.