The 30-year old has signed with the Reds for six months and will be included in the squad for the upcoming Asian Champions League campaign.
Griffiths left the Jets to join Gold Coast United in late November 2008 but after just one game he joined Saudi Arabian club Al Shabab on a lucrative deal.
However, Griffiths' stint in the Middle East did not work out and he has now returned to Australia and will suit up for the Reds, delighting coach Aurelio Vidmar.
"We're really pleased with signing Adam. He's an experienced player, more important he's had experience with Newcastle in the previous Asian Champions League so that's an added bonus for us," he said.
"He's got a lot of strength, he's a good passer of the game, good reader of the game and we can use him in a variety of roles which is really important, so we're really looking forward to Adam rolling up his sleeves and doing his very best for the club.
"Adam's name came across our table about five weeks ago. We also knew at that stage that he was coming back from Saudi Arabia. It's just for the ACL at this point of time, Adam has got other ambitions but we believe it is not out of the question that something might happen in future, but for now the most important thing is that Adam is with us through the Asian Champions League, that's going to be a big positive for us and it will also help with the stimulus and mentality amongst the group in a healthy way.
"Adam is an experienced player having played in the ACL with Newcastle, while he has also made a couple of appearances for the Qantas Socceroos.
"His presence will bring us a lot of strength and he is someone who can play in a variety of roles so we're looking forward to him joining the squad."