Signed last year on a short-term deal, the 36-year-old played 28 times for the West Londoners last season and scored two goals.
Karagounis has 125 caps for Greece and captained the side to victory in the 2004 European Championship after scoring the opening goal of the tournament against hosts Portugal.
Initially released by Fulham last month, he had been linked to a return to Panathinaikos or a move to Australia's Melbourne Victory.
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