GH4079 is a newly developed Ni-based superalloy with a high content of alloying elements and excellent high-temperature mechanical performance. Rare earth (RE) elements are always added to superalloys to improve their stress rupture properties. This study explored how varying additions (0–0.22 wt.%) of lanthanum (La) and cerium (Ce) affected the precipitation and stress rupture performance of the GH4079 superalloy and revealed the related strengthening mechanisms. The addition of RE elements restrained the excessive growth of the γ′ phase to keep its particles fine and uniform, while more RE led to a larger quantity and size of RE-rich precipitates and carbides. At 650 °C and 882 MPa, La and Ce notably boosted the alloy’s stress rupture life. The sample with 0.22 wt.% RE showed optimal overall performance, with a stress rupture life of 179.3 h, more than three times that of the RE-free alloy (55.2 h). The improvement in the stress rupture properties by La and Ce was attributed to beneficial intracrystalline and grain boundary effects. RE reinforced the γ′ phase to impede dislocations and purified the grain boundaries by decreasing the segregation of P and S elements. Additionally, small-sized RE-rich precipitates combined with the fine γ′ phase formed zigzag grain boundaries, alleviating stress concentration and retarding intergranular crack propagation.