Hosted by I'd Do Anything winner Jodie Prenger, the shows will allow thousands of people to take part in musical theatre masterclasses with help from BBC singers and musicians.
The dates include two shows in Leeds, Glasgow and Cardiff, and four at London's Shaftesbury Theatre.
Contestants who have been knocked out of the Andrew Lloyd Webber reality show, which is hunting for a Dorothy, will appear at the performances.
"If you've been singing along on your sofa this is your chance to have a go. Whether you're an enthusiastic amateur or an absolute beginner, we want to get you singing along," said Prenger. "So go on - you've watched the Dorothys - now it's your turn to join in!"
The events, which will last around two hours, are aimed at beginners and will teach singing technique and a range of songs from popular musicals.
On Sunday's results show, former Page 3 model Amy Diamond became the first Dorothy voted off the BBC reality series.
Over The Rainbow continues next Saturday at 7pm on BBC One.