The 35-year-old midfielder was a free agent after leaving Panathinaikos at the end of the 2011-12 campaign - he made 380 appearances for the club in a couple of spells.
Karagounis was a member of the Greek team which won the 2004 European Championship in Portugal and he became their joint-highest capped player in June when he appeared for the 120th time during Euro 2012.
He said: "I'm delighted to have signed for Fulham and I am excited by a new challenge in England and the Barclays Premier League.
"I'm looking forward to working under Martin Jol and playing alongside some fantastic players at this club."
Jol said: "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."
