The 36-year-old made 28 appearances in all competitions for Martin Jol's side last season having joined the club in September 2012
The 36-year-old midfielder was initially released by Fulham at the end of last season when his contract expired after joining in September 2012.
Karagounis, who was part of the Greece side that shocked world football by winning the European Championship in 2004, moved to Fulham as a free agent after leaving Panathinaikos.
He made 28 appearances in all competitions under Martin Jol last season, scoring twice, one of which was a fine chipped effort in an FA Cup tie against Blackpool.
Melbourne Victory and Melbourne Heart were both linked with a move for Karagounis.
Karagounis has enjoyed two spells at Panathinaikos as part of a career that has also included stints at Inter and Benfica.
He has made a record 125 appearances for Greece.