This paper is aimed at exploring the interconversion path between the relaxation modulus E(t) and the corresponding complex modulus E * (ω) for linear viscoelastic solid materials. In contrast to other approximate methods, the fast Fourier transform (FFT) algorithm is directly applied on the time-dependent part of the viscoelastic response R(t). Firstly, the method foundations are presented. Then, a theoretical example is performed by means of a generalized Maxwell model, where the influence of sampling conditions and eventual experimental error and data dispersion is analyzed. Finally, an application example using experimental data is carried out to assess the method. As a result, the proposed procedure allows obtaining the complex modulus by means of relaxation tests, and vice versa.