Two-dimensional (2D) materials, such as graphene and transition metal dichalcogenides (TMDs), possess intriguing properties imparted by their unique atomic-scale structures, and greatly enriched by their various van der Waals (vdW) homo-/heterostructures. Therefore, the precise synthesis of 2D TMDs and their vdW integration with clean interfaces are highly desired, while still challenging. Here, we present a nano-confined chemical vapor deposition approach which enables the atomically-precise synthesis of 2D TMDs and their simultaneous vdW integration with graphene. Within the nano-confinement, 2D TMDs (e.g., NbSe2) that tend to form thick crystals are precisely monolayered owing to an unusual growth kinetics underneath graphene. A sub-monolayer architecture, Janus S-Mo-Se with the polar chalcogen arrangement, is further achieved with the nano-confinement effects. The simultaneous integration of a TMD monolayer with graphene guarantees an ultraclean vdW interface which gives rise to emergent properties. Examples include a conduction enhancement in the graphene/NbSe2 heterostructure and a photomemory effect in the graphene/Janus MoSSe heterostructure. Our results provide a promising platform to realize the atomically-precise synthesis and ultraclean vdW integration of TMD monolayers.