Heteroepitaxy between transition-metal dichalcogenide (TMDC) monolayers can fabricate atomically thin semiconductor heterojunctions without interfacial contamination, which are essential for next-generation electronics and optoelectronics. Here we report a controllable two-step chemical vapor deposition (CVD) process for lateral and vertical heteroepitaxy between monolayer WS2 and MoS2 on a c-cut sapphire substrate. Lateral and vertical heteroepitaxy can be selectively achieved by carefully controlling the growth of MoS2 monolayers that are used as two-dimensional (2D) seed crystals. Using hydrogen as a carrier gas, we synthesize ultraclean MoS2 monolayers, which enable lateral heteroepitaxial growth of monolayer WS2 from the MoS2 edges to create atomically coherent and sharp in-plane WS2/MoS2 heterojunctions. When no hydrogen is used, we obtain MoS2 monolayers decorated with small particles along the edges, inducing vertical heteroepitaxial growth of monolayer WS2 on top of the MoS2 to form vertical WS2/MoS2 heterojunctions. Our lateral and vertical atomic layer heteroepitaxy steered by seed defect engineering opens up a new route toward atomically controlled fabrication of 2D heterojunction architectures.