"It really is a dream come true to join such a famous club."
Rogne continued: "I've already joined training with the first-team for the last few days and I have received a great welcome and have enjoyed very much working with the manager and players at Celtic.
"The Celtic first team is where I want to be and I'll be doing my very best to try and make an impact and ensure that I can achieve this as soon as possible."
Manager Tony Mowbray said: "Thomas is a young player we've watched for a while and we're delighted to bring him to the club. He's only 19 but has had good experience in the Norwegian league.
"We've had a chance to have a look at him in recent days at Lennoxtown and he's shown up well. He has all the physical attributes and personality to be a success at Celtic.
"Thomas has a bright future and will be training with the first-team squad, and competing for a place in the side.
"Like Josh Thompson and Milan Misun, Thomas is a big part of our future plans in defence. We are bringing these talented players to the club in order to ensure the foundations are in place for the coming years."
Even though Rogne is out of contract, his former club Stabaek are entitled to compensation for developing the player.