Oscar Knox from County Antrim, who appeared as the club mascot in a match last summer, had been battling neuroblastoma since 2011.
He became an internet phenomenon as his fight against the disease was shared by his parents, Stephen and Leona, on Twitter.
The couple announced his death yesterday morning, saying: "Our beautiful, amazing and much-loved son, Oscar James Knox gained his angel wings yesterday afternoon. Sleep tight little man."
Mr Lawwell said: "This is absolutely devastating news and our thoughts and prayers are with Oscar's parents and his little sister, Izzie, at this desperately sad time.
"We can't even begin to understand the pain of their loss, but I hope that there will be a small measure of consolation in knowing that there was genuine love and affection for Oscar from the Celtic family throughout the world.
"Oscar's courage throughout his illness was truly inspirational and it was a pleasure for everyone at the club to meet Oscar when he was team mascot last July. This is a very sad day for the Celtic family but, more importantly, for the Knox family, and our thoughts are with them today."