The three-time Austrian champions, who are pushing for a UEFA Europa League spot, attempted to snare Vienna-born Jeggo last June but were rebuffed on that occasion.
However, their persistence has paid off with the Reds relenting and the 23 year-old former Young A-League Player of the Year, set to undergo a medical before joining his new teammates in Turkey ahead of the resumption of the Austrian Bundesliga.
Graz are currently sitting in fourth and Jeggo will be in contention to feature in their first game after the winter break – away go SC Rheindorf Altach on 6 February.
Jeggo’s long-held ambition to play in Europe is now set to be realised with his manager, Sydney-based Buddy Farah, saying: "The boy thoroughly deserves this opportunity after 18 solid months of consistent football since departing Victory to Adelaide.
"He deserves to go to the next level and Graz have been interested in him for quite some time. A good club and a solid league to kick start his European career."
Jeggo, who made 38 appearances for Adelaide after joining them in 2014 from Victory, left Austria for Australia as a 10 year-old when his father landed a job at the CSIRO in Melbourne.