BASE is a novel program for the combined or separate Bayesian analysis of astrometric and radial-velocity measurements of potential exoplanet hosts and binary stars. The tool fulfills two major tasks of exoplanet science, namely the detection of exoplanets and the characterization of their orbits. BASE was developed to provide the possibility of an integrated Bayesian analysis of stellar astrometric and Doppler-spectroscopic measurements with respect to their binary or planetary companions’ signals, correctly treating the astrometric measurement uncertainties and allowing to explore the whole parameter space without the need for informative prior constraints. The tool automatically diagnoses convergence of its Markov chain Monte Carlo (MCMC) sampler to the posterior and regularly outputs status information. For orbit characterization, BASE delivers important results such as the probability densities and correlations of model parameters and derived quantities. BASE is a highly configurable command-line tool developed in Fortran 2008 and compiled with GFortran. Options can be used to control the program’s behaviour and supply information such as the stellar mass or prior information. Any option can be supplied in a configuration file and/or on the command line.