Cavani has been dogged by paparazzi, gossip columns and numerous stories about an alleged affair, but always kept silent until now.
"I started legal proceedings for divorce in Uruguay at the start of February and then continued them in April," he told Espectador.
"By mutual agreement, at the end of last year, we decided our son Lucas would be born in Uruguay, where his mother lives.
"After several months of deep crisis in our marriage, we broke up. Maria Soledad returned to South America to give birth and I had to remain in Naples for professional reasons."