The 38-year-old has the option to extend the deal by one more year if Salernitana are able to retain their Serie A status at the end of the season.
Goodforfans.com reported on Sunday that Salernitana were close to agreeing a deal with the former Galatasaray and Olympique Marseille winger.
Ribery was a free agent after leaving Fiorentina at the end of last season. He scored five goals in 50 Serie A appearances while laying on nine assists for his teammates in two seasons in Florence.
Ribery won nine Bundesliga titles and the UEFA Champions League among numerous other honours during a 12-year stint with Bayern Munich and will bring a lot of experience to the Estadio Arechi side.
"I know the director compared my arrival to that of Maradona at Napoli, but I didn't come here to talk about the titles that I won. When I'm on the field, the trophies I have lifted do not count," said Ribery at his unveiling.
"I feel great and I am available to help Salernitana achieve safety. It's important to find a rhythm immediately, but I am aware that training with the team is very different to personal preparation.
"I am a technical player, but I know the team matters and I have to help the younger players. My role in the locker room will have to be important. Communication makes the difference.
"My mentality is completely different. I need a little time, but starting from tomorrow [Tuesday] I will join the group and I spoke with the medical staff and the coach about getting me ready.
"The passion of the people here is incredible. I will never forget the crowd that was in the stadium for me. I still managed to get excited despite having played in the most prestigious stadiums in the world. It's up to me to repay their trust."
Salernitana are winless in their first two Serie A matches of the season and will travel to Torino after the international break.
