The former Australia manager flew from London on Wednesday afternoon following a period of quarantine in the capital where he met up with Hoops chief executive Dom McKay and watched England host Scotland in their Euro 2020 clash at Wembley.
Postecoglou was appointed Celtic boss on a 12-month rolling contract two weeks ago following a spell at Yokohama F. Marinos.
The 55-year-old made his way to the club's Lennoxtown training ground, although some Celtic players have yet to return from international duty.
Postecoglou will take training for the first time on Thursday and will have 12 days working with the squad before Celtic leave for their pre-season training camp in Wales on July 5th.
The Greek-Australian's first game will be against Sheffield Wednesday on Wednesday, July 7th before three further pre-season friendlies against Charlton Athletic, Bristol City and Preston.
Those matches will be geared towards his first competitive game against Danish side FC Midtjylland in the Champions League second qualifying round at Celtic Park on Tuesday, July 20th.
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