A new series of hybrid compounds with tropinone and thiazole rings in the structure was designed and synthesized as potential anticancer agents. They were tested against human multiple myeloma (RPMI 8226), lung carcinoma (A549), breast adenocarcinoma (MDA-MB-231), and mouse skin melanoma (B16-F10) cell lines. Toxicity was tested on human normal skin fibroblasts (HSF) and normal colon fibroblasts (CCD-18Co). The growth inhibition mechanism of the most active derivative was analyzed through investigation of its effect on the distribution of cell cycle phases and ability to induce apoptosis and necrosis in RPMI 8226 and A549 cancer cells. The tyrosinase inhibitory potential was assessed, followed by molecular docking studies. Compounds 3a–3h show high anticancer activity against MDA-MB-231 and B16-F10 cell lines with IC50 values of 1.51–3.03 µM. Moreover, the cytotoxic activity of the investigated compounds against HSF and CCD-18Co cells was 8–70 times lower than against the cancer cells or no toxicity was shown in our tests, with derivative 3a being particularly successful. The mechanism of action of compound 3a in RPMI 8226 cell was shown to be through induction of cell death through apoptosis. The derivatives show ability to inhibit the tyrosinase activity with a mixed mechanism of inhibition. The final molecular docking results showed for IC50 distinct correlation with experiment.