McCart had a similar role for the last seven years at Motherwell and takes over from Tommy Burns, who died of cancer in May.
"I was honoured to initially have been asked by Tommy to be his assistant," McCart told Celtic's website.
"I enjoyed my time immensely at Motherwell and want to wish everyone at the club the very best for the future."
McCart goes back to Celtic for a second spell as a coach.
Before taking up his previous role at Fir Park, he was part of the Celtic youth development staff.
"It is a real pleasure and privilege to return to Celtic, a club which I have a great affection for," he said.
"I am now looking forward to the many challenges which lie ahead."