We report here the evolution of phase purity in BiFeO3 (BFO) nanoparticles prepared by a novel glycine-assisted combustion method. The study of phase evolution with temperature, in nanoparticles of BFO is carried out using X-ray diffraction (XRD) and thermogravimetry (TG) coupled with differential scanning calorimetry (DSC). Optimum annealing conditions for the synthesis of single-phase BiFeO3 nanoparticles are obtained. The morphology and average grain size of the nanoparticles are determined using a scanning electron microscope (SEM) and an atomic force microscope (AFM), respectively. In situ microanalysis revealed that there are no significant deviations in the stoichiometry of the prepared compound. The magnetic behavior of BFO nanoparticles at 300K has been studied using a vibrating sample magnetometer (VSM). A weak hysteresis loop observed is suggestive of the presence of partially destructed antiferromagnetic arrangement of moments in the material. Low temperature magnetization measurements reveal the presence of spin glass-like transition in the nanoparticles of BFO. A well-developed ferroelectric hysteresis loop has been observed at room temperature at a maximum applied field of 45kV/cm. The nanoparticles of BFO in the present study are found to possess both magnetic and ferroelectric order at room temperature.