In a statement, Verona said former Liverpool and Chelsea forward Borini had signed a deal until the end of the current season, with neither club providing details of the contract.
Borini began his professional career at Chelsea after the Blues signed him from Bologna as a youth prospect.
The 28-year-old went on to play 111 times in the Premier League for the London club, Liverpool and Sunderland, scoring 16 times.
He left Sunderland in 2017 for Milan, where he made 75 appearances in all competitions and scored eight times.
Borini has made one appearance for his national team, in a friendly against the USA in 2012. He was picked for that year's European Championship squad but did not play.