As compared to bulk solids, large surface-to-volume ratio of two-dimensional (2D) materials may open new opportunities for postsynthesis introduction of impurities into these systems by, for example, vapor deposition. However, it does not work for graphene or h-BN, as the dopant atoms prefer clustering on the surface of the material instead of getting integrated into the atomic network. Using extensive first-principles calculations, we show that counterintuitively most transition metal (TM) atoms can be embedded into the atomic network of the pristine molybdenum dichalcogenides (MoDCs) upon atom deposition at moderate temperatures either as interstitials or substitutional impurities, especially in MoTe2, which has the largest spacing between the host atoms. We further demonstrate that many impurity configurations have localized magnetic moments. By analyzing the trends in energetics and values of the magnetic moments across the periodic table, we rationalize the results through the values of TM atomic radii and the number of (s + d) electrons available for bonding and suggest the most promising TMs for inducing magnetism in MoDCs. Our results are in line with the available experimental data and should further guide the experimental effort toward a simple postsynthesis doping of 2D MoDCs and adding new functionalities to these materials.