In this work, we developed a novel fGP-DRT model based on a finite GP approximation that accurately deconvolves the DRT from EIS data. The new model inherits several traits of the previously developed GP-DRT since: 1) it assumes that the DRT is a GP; 2) analysis of synthetic and real experiments shows that this method is consistent; 3) its hyperparameters can be selected by maximizing the experimental evidence; and 4) the fGP-DRT is robust against experimental noise and data truncation. In addition, the fGP-DRT model outperforms the GP-DRT as it can: 1) be constrained to produce only non-negative DRTs; and 2) use both the real and imaginary parts of the impedance. In short, this article develops a new method for the probabilistic analysis of EIS spectra, opening up new research avenues that leverage finite GPs for DRT deconvolution.