The 74 year old comedian, who has Parkinson's disease, will say on ITV that he was treated as a "non-person" at St Peter's Boys School in the Patrick area of Glasgow.
In a one-hour programme later, Dame Judi Dench, Sir Elton John and Peter Kay will be among a host of stars celebrating the work of Connolly.
The writer Armando Iannucci, who attended St Peter's after Connolly, will tell the programme Connolly's routines were considered blasphemous by teachers.
He said: "The head mistress sat us down and told us it was bordering on mortal sin to listen to Billy Connolly because at the time it was full of blasphemous filth.
"Then he became famous and was invited back to the school."
According to ITV, 'Billy Connolly & Me: A Celebration' - which airs at 9pm on Tuesday - will feature the comic sharing "his thoughts on such topics as turning swearing into an art form and the underestimated power of laughter."
St Peter's Boys School is no longer a school, having merged with another school.