Advances in laser beam shaping technologies offer significant benefits for dissimilar metal joining by reducing intermetallic compound (IMC) formation, optimizing weld pool geometry, and improving control over porosity and spatter. However, the relationship between beam shaping, melt pool dimensions, mechanical strength, intermixing, and phase formation requires further investigation. This study examines the effects of different beam shapes and linear energy densities (LED) on melt pool geometry, lap shear joint strength, elemental composition, and phase formation in dissimilar Al–Cu overlap welds. Weld tracks were fabricated using an n-Light Corona system equipped with pure core, core–ring (with varying power-density ratios), and pure ring beam profiles across a wide range of linear energy densities. The results demonstrate that beam shaping significantly influences weld formation and joint integrity, with distinct effects at different LEDs. Joint reliability was assessed via the correlation between peak tensile force and weld cross-sectional area. Elemental analysis confirmed IMC formation and its impact on the mechanical strength of Al/Cu welds, analysed under various beam-shaping conditions. Optimized LED promoted proper fusion with reduced excessive intermixing, while the ring beam induced conduction-mode melting, resulting in a wider joint interface area and superior mechanical strength. For BSI-5 and BSI-6, the reduced heat input at lower LEDs produced an inadequate bonding area at the Al–Cu interface, thereby significantly reducing the joint strength. These findings provide a physical basis for laser beam shaping to widen the stable processing window and produce defect-free, high-quality Al–Cu welds.