Born in Florence, Traballesi received his artistic formation in the Tuscan tradition before relocating to Milan. He became a central figure in the Lombard art scene, eventually serving as a professor at the Brera Academy, where he influenced a generation of artists through his rigorous approach to Neoclassical aesthetics.

His body of work is characterized by both painting and extensive graphic production, including numerous engravings that disseminated Neoclassical motifs. He was particularly noted for his technical precision and his ability to bridge the stylistic transition between late Baroque sensibilities and the emerging Neoclassical movement.

While historical records confirm his significant academic leadership in Milan, contemporary institutional recognition remains focused on his contributions to the history of printmaking and the development of the Brera Academy's curriculum during the late 18th century.