Several aspects of past culture, including historical trends, are inferred from time-based patterns observed in archaeological artifacts belonging to different periods. The presence and variation of these objects provides important clues about the Neolithic revolution and given their relative abundance in most archaeological sites, ceramic potteries are significantly helpful in this purpose. Nonetheless, most available pottery is fragmented, leading to missing morphological information. Currently, the reassembly of fragmented objects from a collection of thousands of mixed fragments is a daunting and time-consuming task done almost exclusively by hand, which requires the physical manipulation of the fragments. To overcome the challenges of manual reconstruction and improve the quality of reconstructed samples, we present IberianGAN, a customized Generative Adversarial Network (GAN) tested on an extensive database with complete and fragmented references. We trained the model with 1072 samples corresponding to Iberian wheel-made pottery profiles belonging to archaeological sites located in the upper valley of the Guadalquivir River (Spain). Furthermore, we provide quantitative and qualitative assessments to measure the quality of the reconstructed samples, along with domain expert evaluation with archaeologists. The resulting framework is a possible way to facilitate pottery reconstruction from partial fragments of an original piece.