A simple extraction method for preparing an organic certifiable stevia extract with high sweetness and optionally with antioxidant properties is provided. The extraction method involves extraction of stevia leaves that have been dried and grinded with a hot solvent generally regarded as safe (GRAS), allowing the dissolution of the sweetening compounds naturally present therein. These sweetening compounds include steviosides and rebaudioside A, which are purified from the extracts by two or more successive chromatographic purifications steps. The sweetening compounds are then eluted with an appropriate elution solvent. The simplicity and organic certification of the method provide advantages over the methods currently employed in the stevia industry.