Additive manufacturing (AM) offers the potential to economically produce customized components with complex geometries. However, the introduction of complex geometry goes hand in hand with the presence of notches. Thus, the basic understanding of the tensile behaviour of AM fabricated notched components must be substantially improved so that the unique features of this rapidly developing technology can be utilized in critical load bearing applications. This work aims to assess the tensile behaviour of different notched specimens manufactured by means of the Electron Beam Melting (EBM) technology and tested in their as-built conditions in order to reveal the interplay between notch geometry and AM specific processing. Scanning Electron Microscopy (SEM) was used to investigate the fracture surface of the broken samples, revealing the presence of process-induced defects, harmfully affecting tensile strength with a reduction of 10% and elongation to failure with 40% with respect to values reported in literature for heat treated AM parts, respectively. Interestingly, the authors have discovered an increase in the tensile strength with the severity of the stress concentrators, quite contrary to what is commonly observed for wrought Ti-6Al-4V. This notch strengthening behaviour particular to AM specimens is related to the influence of defects on the failure driving force. The authors provide a qualitative explanation for this phenomenon using 3D FE analyses together with a theoretical description via the ellipse criterion.