The paper presents the results of numerical and experimental studies of the process of obtaining a permanent joint of two plates of heterogeneous metals that cannot be welded in the usual way: alloy Grade 4 and steel AISI 321 using a laser beam and an intermediate composite insert. The composite insert was obtained by explosion welding of four thin plates of titanium (Grade 4), niobium, copper, and steel (AISI 321). The insert was placed between the welded plates of titanium and steel, and the steel plate was welded with the steel part of the insert, and the titanium plate was welded with the titanium part of the insert. The plates were welded using a CO2 laser. The connection of metals with the help of explosion is carried out without their melting, so the formation of the brittle intermetallics does not occur in most cases. This ensures the greatest strength of the joints as compared to the joints obtained by other welding methods. To analyze the distribution of thermal fields in the composite insert and welded plates, a numerical study was conducted of the laser welding of steel and titanium plates with the corresponding parts of the insert. The purpose of the study was to determine the rational parameters of welding (laser beam power, speed of its movement, size and position of the focal spot), at which there was no complete melting of the steel and titanium parts of the insert during through penetration of the welded plates. The experimental part of the work is devoted to analysis of formation of the internal boundaries and microstructure of the composite insert and the strength of the permanent joint. It is shown that as a result of the explosion welding, weld seams of different wavelike configuration are formed. The most pronounced wavelike boundary is observed in the steel-copper connection, since these materials have a face-centered cubic lattice and are easily subjected to plastic deformation. At the contact boundaries of the plates, transition diffusion zones with different widths (from 5 to 40 μm) and element concentrations are formed. The hardness in the boundary diffusion zones is higher than in the connected metals, which is due to the diffusion interaction of the materials adjacent to each other. It has been established that the tensile strength of the composite insert is comparable to the maximum strength of Grade 4 alloy (456-511 MPa), and the failure in most cases occurred over the least durable component of the composite material, which is the copper plate, whose strength was significantly increased by cold hardening during explosion welding and diffusion of elements of the contacting plates.