Griffiths, who has been without a club since leaving Chinese second-tier outfit Beijing Baxy, has been back in Australia and trained with the Jets earlier this week.
The 32-year-old was hoping to link with the Jets if Nathan Burns was forced to head back to Korean club Incheon United after his loan deal ends this weekend.
"Ryan is an experienced player who Josep (Gombau) feels will suit our game and believes will be a very valuable acquisition adding depth and flexibility to the squad," Adelaide general manager Michael Petrillo said.
Griffiths is expected to arrive in Adelaide on Wednesday night and could be available for Saturday's difficult trip to league leaders Brisbane Roar providing his international clearance comes through in time.
"I would have preferred to stay in Newcastle. I have always tried my hardest for the club and it felt like home but I didn't really want to be second choice," Griffiths said in the Newcastle Herald on Wednesday.
"Adelaide came in with a good offer out of left field. It wasn't my intention to go to another A-League club and I hope the Jets fans forgive me.
"But Adelaide were really keen and made a big effort to get me on board. It was nice to be really wanted."
