The ceremony will take place in a prison lounge usually reserved for legal proceedings, La Gazzetta del Mezzogiorno reported.
Anna Bianco, 42, and Felice Guida, 36, were jailed for four years after breaking into the home of a 90-year-old man and stealing a gold chain from his neck. They have always denied the robbery, the newspaper said.
At the time, they were already engaged and living together.
This is the first wedding to take place in the Bari prison.
After the ceremony, the newlyweds will go back to seeing each other just once a month.