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Double electron−electron resonance (DEER) spectroscopy measures distance distributions between spin labels in proteins, yielding important structural and energetic information about conformational landscapes. Analysis of an experimental DEER signal in terms of a distance distribution is a nontrivial task due to the ill-posed nature of the underlying mathematical inversion problem. This work introduces a Bayesian probabilistic inference approach to analyze DEER data, assuming a nonparametric distance distribution with a Tikhonov smoothness prior. The method uses Markov Chain Monte Carlo sampling with a compositional Gibbs sampler to determine a posterior probability distribution over the entire parameter space, including the distance distribution, given an experimental data set. This posterior contains all of the information available from the data, including a full quantification of the uncertainty about the model parameters. The corresponding uncertainty about the distance distribution is visually captured via an ensemble of posterior predictive distributions. Several examples are presented to illustrate the method. Compared with bootstrapping, it performs faster and provides slightly larger uncertainty intervals.