Two-dimensional transition metal dichalcogenides (TMD) such as MoS2 are promising for applications in novel electronic and optical devices. One major drawback in the device applications of 2D materials, however, is related to their intrinsically anisotropic thermal conductivity in which cross-plane thermal conductivity is more than 10 times smaller than in-plane thermal conductivity. Consequently, cross-plane heat dissipation is not efficient, which has hindered the performance of the 2D devices. Strain has been found to be effective in tuning the band gap of the TMDs, but has yet been investigated in optimizing their thermal transport properties. With about 9% cross-plane compressive strain created by hydrostatic pressure in a diamond anvil cell, we observed about 12 times increase in the cross-plane thermal conductivity of multilayer MoS2. This drastic change arises from the greatly strengthened inter-layer interaction and heavily modified phonon dispersions along the cross-plane direction. The change in electronic thermal conductivity due to semiconductor to metal transition plays a minimal role. Our experimental and theoretical studies show that longitudinal acoustic phonons dominate the increase in cross-plane thermal conductivity under compressive strain; the saturation above 9% strain is associated with the combined effects from enhanced group velocity via the phonon hardening and reduced phonon lifetimes due to phonon unbundling. As a result, the anisotropic thermal conductivity in the multilayer MoS2 at ambient environment becomes almost isotropic under highly compressive strain, effectively transitioning from 2D to 3D heat dissipation. Our observation for the phonon-dominant change of thermal conductivity across the semiconductor-metal transition raises the prospective for designing electronic devices possessing both high electrical conductivity and high cross-plane thermal conductivity for effective heat dissipation, as well as heat modulators with controllable and directional heat flux. The concept for strain tuned 2D to 3D transition in the thermal transport property can be potentially extended to a larger ever increasing family of 2D van der Waals solids.