The right-back, 29, who played for Tunisia at the World Cup, has moved on a free contract after passing a series of stringent medical tests.
Trabelsi's deal with Dutch club Ajax had expired and City boss Stuart Pearce said: "He is one of the best Bosmans (free transfers) of the summer.
The signing is subject to a work permit and the Tunisian is believed to be on a pa-as-you-play deal.
Pearce added on the club's website: "He has played at the highest level for Ajax, and been to three World Cups. He captains his country as well, so it is a good CV.
"I have watched him play for Ajax over the last three years and been very impressed with him.
"He is an attacking full-back we're just waiting on that work permit now."
Trabelsi has been a long-time target of Arsenal and has also been linked with Liverpool and West Ham this summer.
Monaco and Paris St Germain also tracked Trabelsi this summer after he had made it patently clear last season that he would let his contract run out.
"I have been at Ajax for five years," he said in December.
"There are more opportunities in England and I think it's time for me to meet my destiny."

this really best signing of the season.........how did man city snatch him away from arsenal???? damn!!!!

man city made such a good signing