Boyle is played by Rab C Nesbitt actress Elaine C Smith, before the star herself comes on stage for the finale.
Pam Cleggett, 68, travelled from Adelaide, Australia, to watch I Dreamed A Dream with the Susan Boyle fan club.
"Tonight there are 20 states of America represented," she said of the fan club. "And Switzerland, Slovakia, Ireland."
The show had its official opening night on Tuesday at the Newcastle Theatre Royal following several previews.
It follows Boyle's life story from her childhood in West Lothian to her breakthrough performance on ITV1's Britain's Got Talent in 2009 and the subsequent media frenzy.
"I liked it because it's a modern-day fairytale," said the musical's producer Michael Harrison. "But it's a true story because Cinderella did go to the ball." The rags-to-riches story did not shy away from Boyle's difficulties, among them her parents being told she may have brain damage after being starved of oxygen at birth.
It also includes her being beaten up at school and having a breakdown after the Britain's Got Talent final, in which she finished runner-up.
After the life story ended and Smith and her co-stars took the curtain call to a standing ovation, Boyle herself appeared to sing two songs.
The star appeared hesitant at first but developed a rapport with the audience after the first line of I Dreamed A Dream was met with ecstatic applause, as it had been the first time she performed the song on Britain's Got Talent.
That moment from her original talent show appearance was watched online an estimated 500 million times and made her a global superstar virtually overnight.
The new stage musical is designed to feed the devotion to Boyle without requiring her to undergo the rigours of a full concert tour.
The musical will visit 11 cities in the UK and Republic of Ireland and Boyle is expected to make a similar cameo appearance at the end of each show.
Speaking after Tuesday's performance, Elaine C Smith said: "All too often, particularly because of class or poverty or learning difficulties or health difficulties, people are written off, and Susan for me represented the other side to that.
The story has been adapted from Boyle's autobiography and Smith said some lines in the script had come from Boyle herself, such as the description of the frenzy following Britain's Got Talent as being like "a demolition ball crashing through everything I'd ever known".
"At first she really enjoyed it all, all the attention, and then it turned on her in a way," Smith said.
"We didn't want to shy away from that. I didn't want a sugary version of it.
"I was at her 50th birthday party [last April] and I thought, I've got to give you a voice because there are so many people who want to talk for her or put words into her mouth or control her, so it was about finding an authentic voice for her."
One audience member, Pat Lyon, 71, from Hartlepool, described Boyle's appearance as "very emotional".