Objective: This paper presents a Transfer Learning approach for dealing with the statistical variability of EEG signals recorded on different sessions and/or from different subjects. This is a common problem faced by Brain-Computer Interfaces (BCI) and poses a challenge for systems that try to reuse data from previous recordings to avoid a calibration phase for new users or new sessions for the same user. Method: We propose a method based on Procrustes analysis for matching the statistical distributions of two datasets using simple geometrical transformations (translation, scaling and rotation) over the data points. We use symmetric positive definite matrices (SPD) as statistical features for describing the EEG signals, so the geometrical operations on the data points respect the intrinsic geometry of the SPD manifold. Because of its geometry-aware nature, we call our method the Riemannian Procrustes Analysis (RPA). We assess the improvement in Transfer Learning via RPA by performing classification tasks on simulated data and on eight publicly available BCI datasets covering three experimental paradigms (243 subjects in total). Results: Our results show that the classification accuracy with RPA is superior in comparison to other geometry-aware methods proposed in the literature. We also observe improvements in ensemble classification strategies when the statistics of the datasets are matched via RPA. Conclusion and significance: We present a simple yet powerful method for matching the statistical distributions of two datasets, thus paving the way to BCI systems capable of reusing data from previous sessions and avoid the need of a calibration procedure.