Former Italy U21 international Maresca, 32, spent just one season at the Liga club, who are enduring sudden financial difficulties after their owners withdrew funding despite their qualification for the Champions League.
The Serie A club, promoted last season following a shock relegation in 2011, announced the deal on their website.
The former Cagliari trainee, who made his professional debut for West Brom as an 18-year-old, has also played for Juventus, Fiorentina, Sevilla and Olympiacos and scored four Liga goals for Malaga last season.
Maresca becomes the club’s 10th signing this summer as they prepare for life back in the top flight.
Maxi Lopez, Marcelo Estigarribia, Shkodran Mustafi, Gianni Munari, Simon Poulsen, Lorenzo De Silvestri, Eder, Juan Antonio and Tomasso Berni have all arrived at the Genoa-based club so far.