Optical properties of atomically thin transition metal dichalcogenides are controlled by robust excitons characterized by a very large oscillator strengths. Encapsulation of monolayers such as MoSe_{2} in hexagonal boron nitride (hBN) yields narrow optical transitions approaching the homogenous exciton linewidth. We demonstrate that the exciton radiative rate in these van der Waals heterostructures can be tailored by a simple change of the hBN encapsulation layer thickness as a consequence of the Purcell effect. The time-resolved photoluminescence measurements show that the neutral exciton spontaneous emission time can be tuned by one order of magnitude depending on the thickness of the surrounding hBN layers. The inhibition of the radiative recombination can yield spontaneous emission time up to 10 ps. These results are in very good agreement with the calculated recombination rate in the weak exciton-photon coupling regime. The analysis shows that we are also able to observe a sizable enhancement of the exciton radiative decay rate. Understanding the role of these electrodynamical effects allows us to elucidate the complex dynamics of relaxation and recombination for both neutral and charged excitons.