This study proposes an advanced leaching method using organic acids to recover rare earth elements (REEs) from NdFeB permanent magnets from end-of-life computers hard disk drives (HDDs). The end-of-life HDDs were first dismantled in order to recover NdFeB magnets, which were then thermally demagnetized at 350 °C during 30 min before crushing in a ball mill under inert atmosphere. Scanning electron microscopy/energy dispersive X-ray spectroscopy (SEM/EDS) analyses performed on the NdFeB magnets show the heterogeneous structure containing the major matric phase Nd2Fe14B and the REEs-rich phase containing Nd and Pr oxides. Additionally, X-ray diffraction (XRD) and Mössbauer spectroscopy (MS) analyses on the ground NdFeB magnet show that grinding NdFeB magnets under inert atmosphere helps to minimize its oxidation. Chemical analysis shows that the composition of the ground sample is Nd: 22.8 wt%, Pr: 3.3 wt%, Dy: 1.2 wt%, Fe: 62.6 wt%, Co: 1.5 wt%, B: 0.9 wt%, Ni: 0.6 wt%. Diagrams of speciation and equilibrium phases (Eh vs. pH) were calculated to determine the predominance of the formed species in the REEs–organic acids systems. The influence of the organic acid type (acetic acid, formic acid, citric acid and tartaric acid), the acid concentration (10 vol%, up to saturation), and the solid/liquid (S/L) ratio (0.5%–10%) on NdFeB magnets leaching was investigated employing an optimal experimental design conceived by the statistical software JMP. Acetic acid (CH₃COOH) shows the highest leaching performance of REEs, allowing leaching yields over 90% for Nd, Dy and Pr in the acid concentration range of 1.6–10 mol/L and the S/L ratio range of 0.5%–5% at a temperature of 60 °C. The results presented in this investigation suggest that REEs can be recovered from magnets of end-of-life HDDs using an eco-friendly method assisted by organic acids