The young defender has come into Celtic's first-team of late, and has impressed whenever he has been given an opportunity in the starting line-up.
Tierney played for the Bhoys against Fenerbache in the Europa League last week, and he was not overawed by the big stage as he put in a solid display against the Turkish giants.
And Deila said: "I saw that Kieran was a good player from the very first day I watched him. He is a big talent and has shown in training and in the matches he’s played in so far that he can operate at the highest level.
“I had no hesitation in playing him against Fenerbahce. There was not a single thought in my mind about not using Kieran. He showed me what I wanted to see and this is the start of a young man’s career as a Celtic player, take that from me.
“As I said, this is start of a big career for him. Kieran is going to be a big player for Celtic.”
Tierney has now played five times for Celtic's senior side, as he starts to establish his place in the first-team at Parkhead.
The 18-year-old still has time to develop, but he seems set to become a player Deila can shape his team around in the future.
The Norwegian boss has been keen to promote from within ever since arriving at Celtic, and he will be hoping that Tierney's progression can create a path for others to follow.
The Bhoys currently have a number of talented prospects threatening to break through, with Liam Henderson and Callum McGregor also on the fringes of their senior squad.