Euro 2004 winner Karagounis, 35, was a free agent after leaving Panathinaikos in the summer and was thus able to sign for the Whites after the transfer deadline expired at the end of August.
He comes as a direct replacement for fellow 35-year-old Danny Murphy, who left the West London club for relegated Blackburn Rovers after failing to agree a new contract.
Karagounis, who spent 10 years of his career in two spells at Panathinaikos but has also played for Inter Milan and Benfica, spoke of his delight at moving to England with Fulham.
"I'm delighted to have signed for Fulham and I am excited by a new challenge in England and the Premier League," he said. "I'm looking forward to working under Martin Jol and playing alongside some fantastic players at this club."
Manager Jol explained that Karagounis had been brought in for his experience and leadership qualities.
"Giorgos has a wealth of club and international experience and I'm happy that he's joined us for this season.
"He's been an influential player for his club sides and is a renowned player in world football as he's about to become the most-capped player for Greece. He brings many certain qualities to our squad."
Karagounis has played 120 matches for the Greece national team, scoring nine goals. Originally an attacking midfielder, he operates in a deeper role these days but is still a fine free-kick taker.
He was a key player for Greece at this summer's European championships, scoring the winning goal that put his side in the quarter-finals at the expense of Russia, although a booking in that game saw him miss the last-eight defeat to Germany.
Fulham have made several acquisitions following the departures of Murphy and fellow midfielder Dickson Etuhu to Blackburn, and the sales of Clint Dempsey and Moussa Dembele to Tottenham.
Karagounis joins former Manchester United striker Dimitar Berbatov, ex-Wigan hitman Hugo Rodallega, Croatia forward Mladen Petric, Iran winger Ashkan Dejagah, Germany right-back Sascha Riether and former England international Kieran Richardson as new signings at Craven Cottage.
Fulham started their Premier League campaign with a thumping 5-0 win over Norwich but have since slumped to defeats at Manchester United and West Ham and an embarrassing League Cup exit to Sheffield Wednesday.
- Danny Murphy
- Blackburn Rovers