In this study, we investigated the effect of individual and combined applications of manganese (Mn) and zinc (Zn) chelates on common bean grown in hydroponics (nutrient film technique—NFT) on physiological and agronomical responses. Inorganic sulphate forms of Mn and Zn were compared to their synthetic chelate forms, in the replenishment nutrient solution (RNS). Nutrient (N, P, K, Ca, Mg, Fe, Mn, Zn and Cu) to water uptake ratios (termed uptake concentrations; UCs), growth, pods yield and quality, photosynthetic parameters and tissue nutrient status were evaluated in different cropping seasons (spring-summer and autumn-winter crops). Mean UCs of nutrients ranged as follows: 10.1–12.4 (N), 0.8–1.0 (P), 5.2–5.6 (K), 1.8–2.2 (Ca), 0.9–1.0 (Mg) mmol L−1; 12.2–13.4 (Fe), 5.2–5.6 (Mn), 4.4–4.9 (Zn), 0.9–1.0 (Cu) μmol L−1. Tissue macronutrient status remained unaffected in both seasons, however, Mn chelates in the RNS affected Fe within plants. Pod yield and quality, growth, photosynthesis and water uptake did not differ among treatments; however, seasonal variations are presented. Results suggest that the chelate forms of Mn and/or Zn in the refill solution for NFT-grown beans do not lead to any changes, adding superiority in the yield, photosynthesis, and nutritional status of the crops compared to their mineral forms.