Transition metal dichalcogenides (TMDs) are interesting for understanding fundamental physics of two-dimensional materials (2D) as well as for many emerging technologies, including spin electronics. Here, we report the discovery of long-range magnetic order below TM = 40 K and 100 K in bulk semiconducting TMDs 2H-MoTe2 and 2H-MoSe2, respectively, by means of muon spin-rotation (muSR), scanning tunneling microscopy (STM), as well as density functional theory (DFT) calculations. The muon spin rotation measurements show the presence of a 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 sub-percent level. DFT indicates that the antisite defects are magnetic with a magnetic moment in the range of 0.9-2.8 mu_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 opens a path to studying the interplay of 2D physics and magnetism in these interesting semiconductors.