The 20-year-old, who recently made his international debut for Australia, has been with the Hoops at their mid-season training camp in Spain.
Celtic boss Neil Lennon will be delighted he has beaten off competition from English Premier League teams to land Rogic.
"Central Coast Mariners FC wish to officially advise that terms have been agreed for the transfer of Tomas Rogic to Celtic FC," the Australian club said in a statement.
"Subject to Rogic reaching a personal agreement with Celtic, the attacking midfielder will formally be transferred to Neil Lennon's team."
Celtic assistant manager Johan Mjallby is looking forward to working with the player further.
The Swede said: "It is great news Tom is coming back with us and hopefully we will get the deal done. He has been really impressive in training and you can see he has real ability.
"I'm sure Tom watched the games against Barcelona and realised playing for Celtic in the Champions League is second to none.
"It is great for him, too, as Celtic is a team full of young talents who are looking to improve and have great careers. Celtic is a great place for Tom to start in European football."
Fulham, Queens Park Rangers and Reading had also shown interest in Rogic and Mariners football general manager Lawrie McKinna expects the youngster to be a hit at Celtic.
"It's a fantastic opportunity. Celtic's a massive club," McKinna told reporters. "Obviously he has to settle his personal terms with them but the clubs have agreed and it's a great move for him.
"They're playing in the Champions League this year - they'll be playing in the Champions League next year.
"Mark Viduka went there as a stepping stone and it was great for him and, with the style of play there, I think he'll go over and be a standout.
"It puts us on the map with another big club. He's had EPL teams like QPR and Fulham and Reading interested in him as well. It speaks volumes for what the boy has achieved in a year and a half."