The overall performance of joints fabricated using the explosive welding method depends directly on the brittleness of created intermetallic phases and their cohesion with metallic substrates. In this article, we used first principles calculations to show that Sn, V, Cu, and Mg alloying elements present in Ti- and Al-based alloys have a significant influence on the elastic properties and plastic deformation ability of γ-TiAl and Ti3Al. Selected solutes exhibit diversified preferential site occupancy in bulk phases and ordered phase/metallic substrate interface regions. The largest positive effect on ductility and cleavage energy was found for Cu addition (25 pct increase in the B/G ratio), while Sn largely deteriorates cleavage resistance (up to 8 pct). The presented results reveal that further development in the explosive welding field can be reached through the design/application of new alloys composed of elements that improve the properties of the ordered phases present in the joints.