Statistical variability of electroencephalography (EEG) between subjects and between sessions is a common problem faced in the field of Brain-Computer Interface (BCI). Such variability prevents the usage of pre-trained machine learning models and requires the use of a calibration for every new session. This paper presents a new transfer learning (TL) method that deals with this variability. This method aims to reduce calibration time and even improve accuracy of BCI systems by aligning EEG data from one subject to the other in the tangent space of the positive definite matrices Riemannian manifold. We tested the method on 18 BCI databases comprising a total of 349 subjects pertaining to three BCI paradigms, namely, event related potentials (ERP), motor imagery (MI), and steady state visually evoked potentials (SSVEP). We employ a support vector classifier for feature classification. The results demonstrate a significant improvement of classification accuracy, as compared to a classical training-test pipeline, in the case of the ERP paradigm, whereas for both the MI and SSVEP paradigm no deterioration of performance is observed. A global 2.7% accuracy improvement is obtained compared to a previously published Riemannian method, Riemannian Procrustes Analysis (RPA). Interestingly, tangent space alignment has an intrinsic ability to deal with transfer learning for sets of data that have different number of channels, naturally applying to inter-dataset transfer learning.