The 33-year-old defender put pen to paper on a new deal which will see him remain at Genoa until June 2014.
Rossi has also accepted the offer to remain at the club in a managerial role once his playing career is over.
Rossi said: "This is the best present I could have asked for.
"Since joining the club in 2003, I can only say that I have learned so much and I'm proud to remain at the club for life.
"I hope that one day I can give back to others what Genoa has given to me in these years."
The Grifoni go into Saturday's encounter in Sicily on the back of two straight victories.
Genoa followed their 3-2 triumph over Napoli with a 3-2 success over Lazio last time out.
The positive run of form, which has seen them win three of their last four league games, has lifted the Liguria outfit to ninth place.
Genoa coach Pasquale Marino is expected to hand Ze Eduardo a place in attack alongside Rodrigo Palacio at the Angelo Massimino stadium with striker Alberto Gilardino out injured.
Gilardino, who joined Genoa from Fiorentina last month, sustained a muscular injury at the weekend and will be sidelined for four weeks.
To complicate matters for Marino, midfielders Juraj Kucka and Kevin Constant must both serve a one-match ban this weekend.
Rivals Catania are desperate to clinch their first win in 2012 this weekend.
Wednesday's 1-1 draw against Roma extended Catania's winless run to five games and left Vincenzo Montella's outfit in 14th place.
Catania will be bolstered by the return of defender Giovanni Marchese and midfielder Marco Biagianti from suspension.