In this study, a graphene oxide/multi-walled carbon nanotube (GO/MWCNT) based carbon composite was synthesized via the sol-gel method, and its efficacy in the simultaneous removal of three azo dyes—Reactive Black 5, Reactive Red 239, and Reactive Yellow 176—was investigated. Simultaneous measurement of the dyes in solution was performed using multivariate spectroscopic calibration based on Partial Least Squares (PLS) analysis on UV-Vis spectral data. The physicochemical properties of the carbon nanocomposite were characterized using Scanning Electron Microscopy (SEM) and Brunauer-Emmett-Teller (BET) analysis. The influence of various parameters affecting adsorption, including the content of graphene oxide and multi-walled carbon nanotubes in the composite structure, solution pH, and contact time, was optimized using the Response Surface Methodology based on Central Composite Design (RSM-CCD). The maximum removal efficiency was achieved under optimized conditions: a contact time of 90 minutes, an adsorbent dosage of 0.1 g, a composition of 3.8 wt% GO and 2.9 wt% MWCNT, and a pH of 6.5. The corresponding removal percentages for Reactive Black 5, Reactive Red 239, and Reactive Yellow 176 were 96%, 95%, and 92%, respectively. Based on adsorption kinetics data, the adsorption mechanism for Reactive Black 5 (R2 = 0.9837) and Reactive Yellow 176 (R2 = 0.9886) followed the intra-particle diffusion model, whereas Reactive Red 239 (R2 = 0.9909) adhered to the pseudo-first-order kinetic model. The results showed that the adsorption capacity of GO/MWCNT nanocomposite for reactive black 5, reactive red 239, and reactive yellow 176 dyes was 78, 75, and 68 mg/g, respectively. Furthermore, application of the proposed nanocomposite to real textile wastewater obtained from a dyeing company demonstrated its effectiveness in the simultaneous reduction of the studied reactive dyes in aqueous media.