The formation of dissimilar weld joints, including Al/Ti joints, is an area of research supported by the need for weight reduction and corrosion resistance in automotive, aircraft, aeronautic, and other industries. Depending on the cooling rates and chemical composition, rapid solidification of Al/Ti alloys during laser welding can lead to the development of different metastable phases and the formation of brittle intermetallic compounds (IMCs). The effort to successfully join aluminum to titanium alloys is associated with demands to minimize the thickness of brittle IMC zones by selecting appropriate welding parameters or applying suitable filler materials. The paper is focused on the numerical simulation of the laser welding–brazing of 2.0 mm thick titanium Grade 2 and EN AW5083 aluminum alloy plates using 5087 aluminum filler wire. The developed simulation model was used to study the impact of laser welding–brazing parameters (laser power, welding speed, and laser beam offset) on the transient temperature fields and weld-pool characteristics. The results of numerical simulations were compared with temperatures measured during the laser welding–brazing of Al/Ti plates using a TruDisk 4002 disk laser, and macrostructural and microstructural analyses, and weld tensile strength measurements, were conducted. The ultimate tensile strength (UTS) of welded–brazed joints increases with an increase in the laser beam offset to the Al side and with an increase in welding speed. The highest UTS values at the level of 220 MPa and 245 MPa were measured for joints produced at a laser power of 1.8 kW along with a welding speed of 30 mm·s−1 and a laser beam offset of 300 μm and 460 μm, respectively. When increasing the laser power to 2 kW, the UTS decreased. The results exhibited that the tensile strength of Al/Ti welded–brazed joints was dependent, regardless of the welding parameters, on the amount of melted Ti Grade 2, which, during rapid solidification, determines the thickness and morphology of the IMC layer. A simple formula was proposed to predict the tensile strength of welded–brazed joints using the computed cross-sectional Ti weld metal area.