The 20-year-old will join the Scottish champions on a four-and-a-half year deal subject to a work permit application, after a trial period with the club on their trip to Spain
The 20-year-old has been on trial with the club on their mid-season training camp in Spain and will join the Scottish Premier League champions for a fee reported to be around AU$750,000 plus add-ons, subject to a work permit application.
A host of English Premier League clubs, including QPR and Reading, were also said to be keen on the player, but the Hoops have snapped up the player with four international caps to his name.
"We are delighted to announce the signing of Australian Tom Rogic on a four-and-a-half year deal, subject to a work permit," Celtic said in a statement.
"The club can confirm an application will be made to the appropriate authorities in the next couple of days."
Rogic has made 24 appearances for the Mariners, scoring five goals.