The development of a heterojunction nanocomposite leads to improved optoelectronic properties. Herein, ceria (CeO2), copper oxide (CuO), and ceria–copper–copper hydroxide (CeO2-CuO-Cu(OH)2) nanocomposites were prepared via a facile chemical method and their structural, morphological, and optical properties were studied using various characteristic techniques such as X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive X-ray analysis (EDAX), transmission electron microscopy (TEM), ultra-violet visible light absorption (UV-visible), photoluminescence, and thermogravimetry differential thermal analysis (TG-DTA). In the integration of CeO2 and CuO with Cu(OH)2, the band gap is modified to 2.64 eV; this reduced band gap can improve the photocatalytic efficiency of the nanocomposite. The CeO2 can increase light absorption in the nanocomposite, while CuO acts as an electron trap in the composite and this leads to a good enhancement of the optical properties of the CeO2-CuO-Cu(OH)2 nanocomposite. In addition, the heterojunction combination at the interfaces of the CeO2-CuO-Cu(OH)2 nanocomposite facilitates the photo-generated charge separation in the composite, which increases the charge participation in the catalyzed conversion reactions of the prepared composite. The highest photocatalytic degradation efficiencies of 96.4% and 92.7% were achieved for fast green (FG) and bromophenol blue (BP), respectively, using the CeO2-CuO-Cu(OH)2 nanocomposite.