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This work deals with closed form time-domain solutions for the scalar field diffracted by a right-angled dielectric wedge. The approach exploits the knowledge of the frequency-domain expressions for the considered problem, and uses the inverse Laplace transform for obtaining the time-domain diffraction coefficients. These last are involved in the convolution integral expressing the transient diffracted field originated by a pulsed plane wave. The accuracy of the proposed solutions is confirmed by comparisons with data provided by a reliable numerical code based on the Finite Difference Time Domain technique. Although some solutions exist in the frequency domain for the diffraction by dielectric wedges, at the best authors' knowledge, no analytical time domain solutions are available to date.