In this paper, an automatic mesh generator is developed to simulate density-dependent water flow and transport problems in watershed systems. The two-dimensional (2D) triangular mesh is generated by global Delaunay triangulation, and the three-dimensional (3D) triangular-prism mesh is generated by vertical stretch. The implementation procedures of mesh generation are adjusted according to the interaction options of one-dimensional (1D) river, 2D overland, and 3D subsurface flows. An improved boundary point generation algorithm is proposed to maintain appropriate correspondence of points and edges according to the discrete patterns of river reaches and dead ends. Overlapped nodes are generated on zero-width river reaches and zero-width junctions without storage to construct the numerical models for 2D overland simulations. An additional triangular mesh generation method is proposed to create additional triangles for filling the empty water zones of finite-width river reaches, junctions with storage, finite-width ponds, lakes, and dead ends. The boundary loops bounding each water area are identified correctly, and the additional grids are created compatibly, aiming at the finite-depth and zero-depth patterns of storage zones. The computation equations of relevant parameters used for 3D stretch from triangles to triangular-prisms are built, and the 1D/2D/3D correspondence on river reaches, junctions, ponds, lakes, dead ends, and control structures is established. Finally, practical examples for discretizing real-world water areas are provided to demonstrate the robustness and effectiveness of our developed mesh generator by using the skewness as the mesh quality metric.