Motivated by recent observations of unconventional out-of-plane dampinglike torque in WTe2/Permalloy bilayer systems, we calculate the spin-orbit torque generated in two-dimensional transition metal dichalcogenide (TMD)/ferromagnet heterostructures using first-principles methods and linear response theory. Our numerical calculation of spin-orbit torques in WTe2/Co and MoTe2/Co heterostructures shows both conventional and novel dampinglike torkances (torque per electric field) with comparable magnitude, around one hundred ℏ/2e (Ω · cm)-1, for an electric-field applied perpendicular to the mirror plane of the TMD layer. To gain further insight into the source of dampinglike torque, we compute the spin current flux between the TMD and Co layers and find good agreement between the two quantities. This indicates that the conventional picture of dampinglike spin-orbit torque, whereby the torque results from the spin Hall effect plus spin transfer torque, largely applies to TMD/Co bilayer systems.