Karagounis played 28 times for Martin Jol's side last term but was initially released at the end of that campaign.
Franco di Santo's second-half goal earned Wigan a deserved draw away at fellow Premier League strugglers Fulham on Saturday as an entertaining game ended 1-1.
English Premier League club Fulham signed Greece captain Giorgos Karagounis on a free transfer on Tuesday.
Greece on Tuesday played down any wider political significance of their Euro 2012 quarter-final tie against Germany, insisting that they will be more concerned about their opponents on the pitch.
Greece's footballers brought some much-needed and unexpected joy to their hard-pressed compatriots back home on Saturday as they reached the Euro 2012 quarter-finals with a stunning 1-0 win over Russia.
Greece coach Fernando Santos said the country, stricken by the eurozone crisis but buoyed by unexpected progress to the quarter-finals of Euro 2012, deserved respect owing to its proud tradition and history.
Veteran Greece captain Giorgos Karagounis halted Russia's Euro 2012 campaign in its tracks here on Saturday, as the underdogs unexpectedly beat the Group A early pacesetters 1-0 to reach the last eight instead.
Greece captain Giorgos Karagounis is set to equal his country's appearance record of 120 matches in Saturday's must-win group game against Russia at the European Championship.
Co-hosts Poland and Euro 2004 champions Greece fought out an incident-packed 1-1 draw here on Friday in the opening game of the Euro 2012 championship in which both sides finished with just 10 men.
Greece coach Fernando Santos has warned that they will be no pushovers in Euro 2012 while a repeat of their success at the tournament eight years ago could lift an ailing nation desperately in need of a boost.