Persistent and emerging organic pollutants represent a serious and global threat to human health and ecosystems. We describe here a simple, efficient and affordable technology for removing such organic pollutants from aquatic systems. Biosorption process was chosen, meeting these three criteria, and so that biosorbents should be biomass wastes combining the following characteristics: natural, cheap and abundant. Powdered dead roots from invasive alien species (Eichhornia crassipes, Pistia stratiotes and Fallopia japonica), and wastes rich in tannins such as coffee grounds and green tea grounds were tested as biosorbents for removing extensively used organic pollutants: organic UV-filters, insecticides and herbicides. The elemental composition and morphology of the biosorbents were fully determined. The biosorption kinetics for each pair of biosorbent/pollutant was described by a pseudo-second order model. Excellent biosorption efficiency was obtained for 10 μM solution of oxybenzone (89 ± 1%), octocrylene (90 ± 2%), lindane (88 ± 0%) and diuron (90 ± 1%) in only 2 h. And total removal of 10 μM of chlordecone (100 ± 0%) could be achieved, which could be of high concern for the population living in chlordecone-contaminated areas. As such pollutants can be found in aquatic ecosystems, an interference study with salts showed that biosorption efficiency remained as efficient in reconstituted seawater. A principal component analysis was performed as an attempt to rationalise the biosorption results. The solubility of the organic pollutants in water and the concentration of tanins in the biosorbents were key parameters.