Heavy metal contamination is an urgent ecological governance problem in mining areas. In order to seek for a green and environmentally friendly reagent with better plant restoration effect to solve the problem of low efficiency in plant restoration in heavy metal pollution soil. In this study, we evaluated the effects of three biodegradable chelating agents, namely citric acid (CA), fulvic acid (FA) and polyaspartic acid (PASP), on the physicochemical properties of copper tailings, growth of ryegrass (Lolium perenne L.) and heavy metal accumulation therein. The results showed that the chelating agent application improved the physicochemical properties of copper tailings, increased the biomass of ryegrass and enriched more Cu and Cd in copper tailings. In the control group, the main existing forms of Cu and Cd were oxidizable state, followed by residual, weak acid soluble and reducible states. After the CA, FA or PASP application, Cu and Cd were converted from the residual and oxidizable states to the reducible and weak acid soluble states, whose bioavailability in copper tailings were thus enhanced. Besides, the chelating agent incorporation improved the Cu and Cd extraction efficiencies of ryegrass from copper tailings, as manifested by increased root and stem contents of Cu and Cd by 30.29–103.42%, 11.43–74.29%, 2.98–110.98% and 11.11–111.11%, respectively, in comparison with the control group. In the presence of multiple heavy metals, CA, FA or PASP showed selectivity regarding the ryegrass extraction of heavy metals from copper tailings. PCA analysis revealed that the CA-4 and PASP-7 treatment had great remediation potentials against Cu and Cd in copper tailings, respectively, as manifested by increases in Cu and Cd contents in ryegrass by 90.98% and 74.29% compared to the CK group.