The study of the influence of phase transformations on residual stresses in heterophase materials is very important for predicting the service life of machines and constructions. Welded joints made of dissimilar materials are of particular interest. The chemical and phase compositions, microstructure, microhardness, strength, and fracture surface characterization of dissimilar AISI 321/Cu/Ti laser joints have been studied. Distinctive features of the laser welding conditions are the displacement of the focal spot to the steel/Cu interface and the deepening of the focus by 3 mm. The chosen mode of laser welding made it possible to obtain the following chemical composition of the melting zone (MZ): 55.3 wt% Cu, 32.2 wt% Fe, 8.5 wt% Cr, 4.0 wt% Ni, and 1.0 wt% Ti. After crystallization in MZ, two supersaturated solid solutions are formed: one based on copper and the other based on iron. During post-welding cooling, (Fe,Cr)2Ti intermetallic particles sized 10 nm homogeneously precipitate in the Cu-based solid solution, and 10-nm TiCu4 particles precipitate in the Fe-based solid solution. Fe-based regions become additionally hardened (to 540 HV 0.025) due to the formation of martensite crystals in the austenite matrix. Alloying of titanium with copper causes βTi stabilization at the interface Ti/MZ. During contact melting of titanium, Ti2Cu intermetallic particles of three types emerged: from 2 to 5 μm eutectic, from 0.1 to 0.5 μm eutectoid, and those homogeneously precipitated in βTi during cooling, sized 10 nm. After quickly cooling, the compressive residual stresses formed in the welded joint. When specimens with welded joints were tensile tested, they fractured in the MZ according to a mixed type. Ductile fracture occurred in Cu- and Fe-based microconstituents by the MZ zone; brittle fracture occurred in the zone with (βTi + Ti2Cu) structure near Ti. The ultimate tensile strength of the resulting welded joints is 470–515 MPa, and this significantly exceeds the available data.