Plant polyphenols are a huge group of compounds with a wide spectrum of applications. Substances from this group have been used in polymer materials such as stabilizers, dyes, indicators, fungicides, and bactericides, especially in new generation packaging materials. The aim of this study is to obtain environmentally friendly materials based on the biodegradable aliphatic polyesters, polylactide (PLA) and polyhydroxyalkanoate (PHA), with plant functional additives, (+)-catechin and polydatin. These natural polyphenols (polydatin and (+)-catechin) have not been used so far in polymer materials (especially in biodegradable polyesters) as stabilizers, dyes, and indicators of aging. The application of polydatin and (+)-catechin as multifunctional additives for biodegradable polymers is a scientific novelty. This paper presents the following analyses of polyester materials: SEM microscopy, wide angle x-ray diffraction, mechanical properties, thermal analysis, surface free energy analysis, and determination of change of color after controlled UV exposure, thermal oxidation and weathering. Both PLA and PHA polyesters were characterized by higher resistance to oxidation and greater resistance to degradation under the influence of UV radiation. In addition, (+)-catechin was used simultaneously as a dye and an indicator of the aging time of polymeric materials. In contrast, polydatin did not dye polymers, but was a very good indicator of their lifetime, changing color under the influence of various external factors. Both polyphenols can be successfully used as natural additives for pro-ecological polyesters.