The 16-year-old, who is a left-sided centre-half, joins from Rosenborg and has been capped by his country at Under-16 level.
Hjelde is the son of former Nottingham Forest, Mansfield Town and Rosenborg defender Jon Olav Hjelde, and will initially join the Parkhead club's reserve team, with a view to progressing to the first team.
Hjelde told the club's website: “It is a real honour to join Celtic, I had a number of options in front of me, but I know that Celtic is the right place for me.
"I have had the opportunity to speak to many people within the club, including the manager, Neil Lennon, and that has been fantastic.
“I know that the club will provide me with the best pathway for my future and I am really looking forward to the next few years of my career at such a fantastic club."