Lung cancer is a major public health concern, with a high incidence and fatality rate. Its treatment is very difficult, as it is mostly diagnosed in advanced stages. Non-small cell lung carcinoma (NSCLC) is the major form of lung carcinoma that persists. Brigatinib (BGT), a powerful small-molecule tyrosine kinase inhibitor, has demonstrated significant therapeutic potential in the treatment of NSCLC with anaplastic lymphoma kinase (ALK) mutations. However, the therapeutic applicability of BGT is hampered by its low solubility and bioavailability. In this study, we developed a mixed micelle system comprising Soluplus and TPGS loaded with BGT. BGT was encapsulated into the mixed micelles using various combinations of Soluplus and TPGS, with encapsulation efficiency (EE%) ranging from 52.43 ± 1.07 to 97.88 ± 2.25%. The dynamic light scattering data showed that the mixed micelles ranged in size from 75.7 ± 0.46 to 204.3 ± 5.40 nm. The selected mixed micelles (F6) showed approximately 38% BGT release in the first 2 h, and subsequently, within 72 h, the release was 94.50 ± 5.90%. The NMR experiment confirmed the formation of micelles. Additionally, the mixed micelles showed significantly higher cellular uptake (p < 0.05) and increased cytotoxicity (p < 0.05) as compared to the free BGT. Specifically, the obtained IC50 values for BGT-loaded Soluplus-TPGS mixed micelles and free BGT were 22.59 ± 6.07 and 61.45 ± 6.35 μg/mL, respectively. The results of the in vitro stability experiment showed that the selected mixed micelle (F6) was stable at both room temperature and 4 °C, with only minor changes in size and PDI. Our results indicate great potential for the developed Soluplus-TPGS mixed micelles as a delivery system for BGT.