The former IK Start midfielder has joined on a four-year deal.
“In my head I have dreamed about that (the crowd) so many times since I signed for Celtic," said Ajer.
"Here in Norway we have five or six thousand at each game and at Celtic there will be 50-60,000 at some games so that will be crazy. For me it’s a big dream come true to play in front of so many people.
Celtic fans in the stadium await the arrival of New Celtic manager Brendan Rodgers after the press conference
“I’m most looking forward to just being a professional footballer and living out my dream, to walk out at Celtic Park in front of thousands of supporters and hopefully score some goals and celebrate in front of so many people,” he added.
The talented Norwegian will add depth to the Hoops midfield and has undoubted potential for development in the coming years.
Ex-Celtic manager Ronny Deila
Ronny Deila was responsible for bringing Ajer to the club after signing the youngster on a pre-contract agreement in January, before being relieved of his duties this summer.
The 18-year old will now be tasked with impressing new boss Brendan Rodgers enough in pre-season to convince the former Liverpool boss that he deserves a place in the first-team squad next season.
Celtic - Brendan Rodgers Press Conference
Rodgers will be keen to make his mark on the Celtic squad and build one capable of adopting his philosophy and style of play.
The next few months will likely see a swell of transfer activity as Rodgers welcomes new recruits and waves goodbye to those deemed unfit for purpose, and the likes of Ajer, Scott Allan and Ryan Christie will need to perform in pre-season if they are to play a role next term.