If all goes smoothly, the Aussie midfielder could even become Neil Lennon's second January transfer signing within 24 hours, joining loan defender Rami Gershon.
Rogic watched the Celtic players he hopes to be joining defeat Steaua Bucharest 2-1 in Marbella last night.
This morning he packed his bags to accompany them on the flight back to Glasgow after their week-long training camp on the Costa Del Sol.
Celtic are confident they have made a positive impression on the 20 years old. And, having agreed a fee of £490,000 with his club, Central Coast Mariners, the Hoops hope to get the deal over the line before any of the others chasing the rising star can hijack the deal.
Cash-strapped Mariners are desperate to get top dollar for their player, who is out of contract in May.
He could sit tight and walk away for free then, but all parties are keen to compete a deal now.
Personal terms are the final hurdle to overcome, and Celtic are confident they can meet his requirements.
Neil Lennon, who hopes to be part of the welcoming committee waiting on Rogic when he arrives here, has been absent from the Hoops camp since Sunday as he attended a manager's seminar in England.
But his assistant, Johan Mjallby, could not hide his delight that agreement has been reached to allow Rogic to travel to Glasgow and what everyone hopes swill be a successful conclusion to the battle to sing the talented kid.
"It's great news he's coming back with us and, hopefully, we'll get the deal," said Mjallby.
"He's been really impressive in training, and you can see he has real ability. I hope that it will go in our favour.
"I'm sure he watched the games against Barcelona, and playing for Celtic in the Champions League is second to none.
"Celtic is a great place for Tom to start in European football."
Mariners are resigned to losing their player, who would have headed back to Oz today to prepare for his return to action at the weekend following a three-game ban had agreement not been reached with Celtic over a transfer fee.
The serious interest from QPR, Fulham, Reading, Brugge, Rayo Valecano and Celta Vigo has been headed off by the Hoops' prompt action.
Mariners director of football, former Kilmarnock player Lawrie McKinna, is not surprised that the youngster has impressed and predicts he will be a smash at Celtic.
Rogic has shown in his short A-League career that he can do that with ease, and the 6ft 2in Australian international has the added attraction of being powerful in the air.
Ayrshire-born McKinna said: "I think he's going to be a big hit over there, because he's something different.
"It's a hard-working, grafting league, and for him to go there with his silky touch, I think he could be a stand-out and something special."