Yeast Saccharomyces cerevisiae biomass was applied for rhenium and accompanying elements (copper and molybdenum) removal from single- and multi-component systems (Re, Re-Mo, Re-Cu, and Re-Mo-Cu). Yeast biomass was characterized using X-ray diffraction, scanning electron microscopy, and Fourier transform infrared spectroscopy. The effects of biosorption experimental parameters such as solution pH (2.0–6.0), rhenium concentration (10–100 mg/L), time of interaction (5–120 min), and temperature (20–50 °C) have been discussed in detail. Maximum removal of rhenium (75–84%) and molybdenum (85%) was attained at pH 2.0, while pH 3.0–5.0 was more favorable for copper ions removal (53–68%). The Langmuir, Freundlich, and Temkin isotherm models were used to describe the equilibrium sorption of rhenium on yeast biomass. Langmuir isotherm shows the maximum yeast adsorption capacities toward rhenium ions ranged between 7.7 and 33 mg/g. Several kinetic models (pseudo-first-order, pseudo-second-order, and Elovich) were applied to define the best correlation for each metal. Biosorption of metal ions was well-fitted by Elovich and pseudo-first-order models. The negative free energy reflected the feasibility and spontaneous nature of the biosorption process. Saccharomyces cerevisiae biomass can be considered as a perspective biosorbent for metal removal.