The former Australia boss has been holed up in London since last week while completing a quarantine stint after jetting in from Japan.
But the 55-year-old is now preparing to get to work on reshaping the Hoops in his image after touching down in Scotland at last.
He will get to meet his players face to face on Thursday as he takes his first training session at their Lennoxtown base.
The ex-Yokohama F Marinos boss has no further time to waste, with Celtic's opening Champions League qualifier against Danes Midtjylland just four weeks away.
But Postecoglou is ready to put the graft in.
"It's great to be here," he said. "It's been a tough three weeks to get here but I'm super happy to be here now.
"It's been a bit of a whirlwind and I knew it wouldn't sink in that I'm the new Celtic manager until I got here. Now I can get cracking and start working.
"I got to meet everyone and put everything in place that we need to. It's been fantastic.
"I already had some familiarity with it but it's a great set-up. The people here are fantastic and I'm looking forward to working with everyone.
"Everyone keeps warning me about the weather but it all looks pretty beautiful at the moment."
Postecoglou held talks in London with new Hoops chief executive Dom McKay last week before going to watch a number of his new players in action for Scotland against England at Wembley.
He has also held virtual video meetings with a number of players as he sets about getting to know his new squad.
Now he will look to put his points across on the training pitch as the real work gets started.
Postecoglou - who was appointed Celtic boss on a 12-month rolling contract - will have 12 days to get his side used to his methods before Celtic leave for their pre-season training camp in Wales on July 5.
The Greek-Australian's first game will be against Sheffield Wednesday on Wednesday, July 7, with three further pre-season friendlies against Charlton, Bristol City and Preston lined up before the crunch qualifier with Midtjylland.
And Postecoglou believes the personal touch will ensure his team are ready to go.
"I'm not a fan of Zoom even though it's been our existence for 18 months so I was keen to get up here as soon as possible," said Postecoglou.
"I had to do quarantine and make sure we followed all the protocols but being here now is exactly where I wanted to be.
"Ultimately, people want to get to know me. It's one thing to have ideas and talk about what you want to do but people need to meet me and understand me as a person as much as a manager. You can't do that unless you meet people in person and we'll start that process now."