Two-dimensional (2D) semiconductors, in particular transition metal dichalcogenides (TMDCs), have attracted great interest in extending Moore’s law beyond silicon^{, –}. However, despite extensive efforts^{, , , , , , , , , , , , , , , , , , , , –}, the growth of wafer-scale TMDC single crystals on scalable and industry-compatible substrates has not been well demonstrated. Here we demonstrate the epitaxial growth of 2 inch (~50 mm) monolayer molybdenum disulfide (MoS₂) single crystals on a C-plane sapphire. We designed the miscut orientation towards the A axis (C/A) of sapphire, which is perpendicular to the standard substrates. Although the change of miscut orientation does not affect the epitaxial relationship, the resulting step edges break the degeneracy of nucleation energy for the antiparallel MoS₂ domains and lead to more than a 99% unidirectional alignment. A set of microscopies, spectroscopies and electrical measurements consistently showed that the MoS₂ is single crystalline and has an excellent wafer-scale uniformity. We fabricated field-effect transistors and obtained a mobility of 102.6 cm² V⁻¹ s⁻¹ and a saturation current of 450 μA μm^–1, which are among the highest for monolayer MoS₂. A statistical analysis of 160 field-effect transistors over a centimetre scale showed a >94% device yield and a 15% variation in mobility. We further demonstrated the single-crystalline MoSe₂ on C/A sapphire. Our method offers a general and scalable route to produce TMDC single crystals towards future electronics.