The former Greece Under-21 cap had his contract terminated by the Greek Superleague club last week.
Skondras joined PAOK from Atromitos in 2013 and has made 94 appearances for the Thessaloniki-based club.
But he has not played at all this season after Vladimir Ivic took over as head coach.
Skondras is unlikely to receive international clearance in time to play for Hamilton in Tuesday's Scottish Premiership game against Inverness Caledonian Thistle.
The defender, who has played for PAOK in the Champions League and Europa League, becomes the second player to sign for a Scottish club on Monday after leaving PAOK.
Former team-mate Alexandros Tziolis, the Greece midfielder,  joined Hearts until the end of the season.
Accies player-manager Martin Canning is also on the look-out for a striker but says he may have to leave it late as Tuesday's 23:00 GMT transfer deadline looms.
"I'm still speaking to a couple of strikers that I'd like to get in, but they will be last minute things if they end up going through," he said.
However, he does not expect to be waving goodbye to top scorer Ali Crawford any time soon.
The midfielder has nine goals this season but missed a glorious chance to put Hamilton in front against St Johnstone on Saturday in a game Accies went on to lose 3-0 in Perth.
And his boss reckons he will need to start putting those kind of opportunities away if he wants to make a move to a bigger club.
"There has been literally no-one contacting the club about Ali," said Canning.
"I think his agent has asked how much we would accept for him, but that's the only question that has ever been put to us.
"Hopefully that opportunity will come for Ali, but he has got to keep his head down and continue to work hard and, if you look at Saturday's game, take the chances that will put him in the spotlight.
"Over the last three or four games, he's had big opportunities to score important goals and, had he done that, I'm sure we'd be sitting here with an offer in for him.
"Big players take those chances and that's what kicks you on to the next level."
Greek right-back Giannis Skondras has joined Hamilton Academical until the end of the season after the 26-year-old left PAOK Salonica.