Layered structures of transition metal dichalcogenides stacked by van der Waals interactions are now attracting the attention of many researchers because they have fascinating electronic, optical, thermoelectric, and catalytic properties emerging at the monolayer limit. However, the commonly used methods for preparing monolayers have limitations of low yield and poor extendibility into large-area applications. Herein, we demonstrate the synthesis of large-area MoSe2 with high quality and uniformity by selenization of MoO3 via chemical vapor deposition on arbitrary substrates such as SiO2 and sapphire. The resultant monolayer was intrinsically doped, as evidenced by the formation of charged excitons under low-temperature photoluminescence analysis. A van der Waals heterostructure of MoSe2 on graphene was also demonstrated. Interestingly, the MoSe2/graphene heterostructures show strong quenching of the characteristic photoluminescence from MoSe2, indicating the rapid transfer of photogenerated charge carriers between MoSe2 and graphene. The development of highly controlled heterostructures of two-dimensional materials will further promote advances in the physics and chemistry of reduced dimensional systems and will provide novel applications in electronics and optoelectronics.