• Thomas Rogne in training last week at Celtic's Lennoxtown training complex
The 19-year-old, who signed on free transfer, has been training with the Parkhead side over the past week.
Celtic are reported to have paid 220, 000 in compensation to the youngster's former club.
The Norway Under-21 cap is expected to partner up with Jos Hooiveld in Celtic's central defence following his 2 million move from AIK Stockholm.
Celtic 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.
"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."
Rogne rejected an extension to his contract with Stabaek plus approaches from clubs in Norway to sign for the Parkhead side.
"I 'm absolutely delighted to sign for a club of Celtic's stature, he told the Celtic website.
"It really is a dream come true to join such a famous club.
"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."