Transition metal dichalcogenides (TMDs) are interesting for understanding the fundamental physics of two-dimensional (2D) materials as well as for applications to many emerging technologies, including spin electronics. Here, we report the discovery of long-range magnetic order below T_M = 40 and 100 K in bulk semiconducting TMDs 2H-MoTe₂ and 2H-MoSe₂, respectively, by means of muon spin rotation (μSR), scanning tunneling microscopy (STM), and density functional theory (DFT) calculations. The μSR measurements show the presence of large and homogeneous internal magnetic fields at low temperatures in both compounds indicative of long-range magnetic order. DFT calculations show that this magnetism is promoted by the presence of defects in the crystal. The STM measurements show that the vast majority of defects in these materials are metal vacancies and chalcogen-metal antisites, which are randomly distributed in the lattice at the subpercent level. DFT indicates that the antisite defects are magnetic with a magnetic moment in the range of 0.9 to 2.8 μ_B. Further, we find that the magnetic order stabilized in 2H-MoTe₂ and 2H-MoSe₂ is highly sensitive to hydrostatic pressure. These observations establish 2H-MoTe₂ and 2H-MoSe₂ as a new class of magnetic semiconductors and open a path to studying the interplay of 2D physics and magnetism in these interesting semiconductors.