The comedian will appear at the SECC Clyde Auditorium on October 29 and 30, adding two new shows to the original line-up of seven.
People started queuing outside the Music Hall in Aberdeen at around 4am this morning to get their hands on tickets for his first two shows.
The High Horse tour starts in the city on September 29 before travelling to Perth, Edinburgh, Dundee and Glasgow.
The comedy tour is his first in Scotland for five years and comes after the "Big Yin" revealed he had been diagnosed with Parkinson's disease and prostate cancer.
He has now been given the all-clear from cancer, and the 71-year-old has vowed to continue with his stage and acting work.
Aberdeen Performing Arts manager Joyce Summers said the ticketing website struggled under demand as the 2,600-seat capacity shows sold out in 50 minutes.
"We knew this was going to be a busy day - the queue outside the Music Hall started at 4.15am," she said.
"We sympathise with those who were disappointed, but we made every effort to maximise box office capacity and continually monitored the situation. The website struggled with the sheer volume of traffic at one point.
"We are now looking forward to welcoming Billy Connolly to the Music Hall for two great shows to kick off his High Horse tour.
"The previous fastest selling show at the Music Hall was for Emile Sande's first homecoming gig last year which sold out within 47 minutes - but that was for a single show."
There were also queues in Edinburgh and Dundee for tickets, while demand caused payment delays online.
In an interview earlier this year, Connolly said he was "angry" about claims that the drugs he had to take for Parkinson's caused on-stage memory loss during a show in Belfast last year.
''I've lost my train of thought all (through) my career. It's what makes me different from everybody else - 'Where was I, what was I saying?' 'I just ramble off and come back ages later.''
The Glaswegian said he uses notebooks to improve his memory.
''I've put myself on a strict regime of crossword books. They remind me of everything. I have to train my memory,'' he said.
''I've got a notebook with all the words I tend to forget. It's the same ones cropping up again and again.''