The Scottish giants have zeroed in on the Australian as the man they want to lead the fightback against rivals Rangers next season.
Postecoglou is keen to answer the call and Celtic have applied for UEFA for an exemption for him to manage in Europe due to his lack of a UEFA Pro License.
Now the move has taken another step forward as Celtic have thrashed out a compensation fee for Postecoglou.
The Scottish side have agreed a figure with Yokohama F. Marinos to release Postecoglou from his contract at the club.
Postecoglou will leave Yokohama F. Marinos sitting in third place in the Japanese top flight.
Pre-season is now looming for Celtic and Postecoglou will be keen to make his way to Scotland as soon as possible.
Celtic will also be involved in European qualifiers and Postecoglou will want to hit the ground running.