Joining an additively manufactured component to a forged or cast part through welding processes has recently attracted the attention of engineers and scientists. This technique integrates the technical benefits of additive manufacturing (AM) technology with conventional processes that may be more cost-efficient. In this paper, the effect of residual stresses on the mechanical performance of a hybrid welded pipe joint connecting an additively manufactured maraging steel (MS1) pipe segment with a conventional P20 steel tube having an equivalent outside diameter was studied. A sequentially coupled thermo-mechanical continuum finite element (FE) modeling procedure to predict the residual stress state on circumferential pipe hybrid MS1-P20 joints subjected to multi-axial loads was developed and validated. Available experimental data on a welded pipe joint with conventional stainless steel (SUS304) were used to calibrate the model. The FE modeling procedures were further validated for the hybrid MS1-P20 joint. The predicted residual stress state was mapped on the pipe joint with equal and unequal wall thickness joint transitions. The mechanical performance of these pipe joints was evaluated with the application of internal pressure, uniaxial tension, and flexural loads. The major contribution of this study was the proposition of a new concept of hybrid joints, where a significant transition of the load was expected. The new hybrid joint concept was presented to meet the existing design criteria requirements without sacrificing other parameters (e.g., component weight and manufacturing expense) and facilitate the production of hybrid components using AM techniques.