Lignin is natural and renewable polymer, the second most abundant on Earth. Properly used it can reduce synthetic and oil based materials in addition to contributing to the biodegradable systems. In this work, the kraft lignin was subjected to gamma radiation at absorbed doses of 30, 60, and 90 KGy in order to increase the interaction with “Poly(butylene adipate‐co‐terephthalate) (PBAT)/Poly(lactic acid) (PLA)” blend (Ecovio®). PBAT/PLA/lignin blends with 10% of the weight of lignin were produced by extrusion using twin‐screw extruder and characterized by Fourier transform infrared spectroscopy (FTIR), Differential scanning calorimetry (DSC), and Field emission scanning electron microscopy (FE‐SEM). FTIR spectra showed partial miscibility between PBAT/PLA and lignin, most due to the hydrogen bond between PBAT/PLA carbonyl and lignin hydroxyl, being intensified in irradiated lignin compounds. As evidenced on DSC scans, in PBAT/PLA/irradiated lignin the crystallization peak was shifted to lower temperatures and the crystallization rate decreased. Crystallization kinetics was modeled using Pseudo Avrami, and isoconversional models of Friedman and Vyazovkin. Pseudo‐Avrami displayed linearity deviation at beginning and crystallization ending due to the nucleation and secondary crystallization, while from Friedman and Vyazovkin the activation energy (Ea) was higher for PBAT/PLA/irradiated lignin 30 KGy, characterizing crystallization with higher energy consumption. FE‐SEM images showed better dispersion and miscibility in PBAT/PLA/irradiated lignin. The results indicate that the irradiation of Kraft lignin promotes miscibility and compatibility of PBAT/PLA/lignin.