The 18-year-old is tipped for big things at Parkhead and The Bhoys wasted little time in offering him professional terms.
Wallace inked a four-year contract on Monday and will now look to force his way into Martin O`Neill`s first-team plans in the seasons ahead.
He told the club`s website: "To be honest it didn't take me very long at all to weigh up the pros and cons of signing on with Celtic.
"I'm here now until I will be 22, so I want to use that time to step up the ladder.
"A few of the lads in the Under-21s will be moving on this close season so hopefully I will become more of a regular there but I think I'll have to be a bit more patient when it comes to the first-team."
