The former Yokohama F Marinos coach has been self-isolating in London since touching down in the UK last week.
Now he is preparing to travel north to take his first up-close look at the team he has inherited from Neil Lennon.
Celtic appointed the Greek-born Australian last week having spent more than three months trying to entice Eddie Howe to Glasgow.
But Postecoglou has just four-and-a-half weeks left to get the Hoops up to speed for their opening Champions League qualifier against Danish outfit Midtjylland on July 20.
However, he has already held face-to-face talks with Dominic McKay after the in-coming Hoops chief executive travelled south on Friday to meet him, with the pair determined to step up their preparations for the new campaign.
Celtic said in a statement: "After travelling to the UK from Japan, Celtic manager Ange Postecoglou has completed the required initial period of quarantine, through the UK Government test to release scheme in England and has been straight down to work with incoming chief executive Dom McKay.
"Ange and Dom met in London today to continue working on preparations for the new season.
"Ange will also watch his Celtic stars within the Scotland squad take on England at Wembley this evening.
"It is planned that Ange will be in Glasgow next week as the bulk of the first team playing squad returns for pre-season training.
"After a period of training at Lennoxtown, Ange and the squad will then travel to our training camp in Wales, from July 5-14."