We propose a novel evolutionary algorithm on bit vectors which derives from the principles of information theory. The information-theoretic evolutionary algorithm (it-EA) iteratively updates a search distribution with two parameters, the center, that is the bit vector at which standard bit mutation is applied, and the mutation rate. The mutation rate is updated by means of information-geometric optimization and the center is updated by means of a maximum likelihood principle. Standard elitist and non elitist updates of the center are also considered. Experiments illustrate the dynamics of the mutation rate and the influence of hyperparameters. In an empirical runtime analysis, on OneMax and LeadingOnes, the elitist and non elitist it-EAs obtain promising results.