Two-dimensional (2D) MoS2, which has great potential for optoelectronic and other applications, is thermodynamically stable and hence easily synthesized in its semiconducting 2H phase. In contrast, growth of its metastable 1T and 1T' phases is hampered by their higher formation energy. Here we use theoretical calculations to design a potassium (K)-assisted chemical vapour deposition method for the phase-selective growth of 1T' MoS2 monolayers and 1T'/2H heterophase bilayers. This is realized by tuning the concentration of K in the growth products to invert the stability of the 1T' and 2H phases. The synthesis of 1T' MoS2 monolayers with high phase purity allows us to characterize their intrinsic optical and electrical properties, revealing a characteristic in-plane anisotropy. This phase-controlled bottom-up synthesis offers a simple and efficient way of manipulating the relevant device structures, and provides a general approach for producing other metastable-phase 2D materials with unique properties.