"The human remains belong to Maria Grazia Trecarichi," Grosseto prosecutor Francesco Verusio said.
The remains were found on October 8th and were tested by DNA specialists in Rome.
Thirty bodies were recovered from the wreck after the cruise liner crashed off the tiny island of Giglio in Tuscany on January 13th 2012, but two - mother of one Trecarichi and Indian waiter Russel Rebello - were still officially reported missing.
La Repubblica newspaper said fragments of bone collected separately "have yet to be tested but could belong to Rebello".
Trecarichi's widower Elio Vincenzi said: "I have learned from the press that the remains belong to my wife but have had no official confirmation. They assured me I would be the first to know, it didn't go that way."
He had earlier identified shoes and a necklace found with the remains as belonging to his wife.
The search for the wreck's two remaining bodies began in late September after the 114,500-ton ship was lifted upright in the biggest salvage operation of its kind.
The ship's captain, Francesco Schettino, is on trial for multiple manslaughter, abandoning ship before all the passengers had been evacuated and causing environmental damage.
The Costa Concordia crashed into a group of rocks after Schettino allegedly performed a risky "salute" manoeuvre just off Giglio with 4,229 people from 70 countries on board.