Graeme Garden, Tim Brooke-Taylor, Barry Cryer and Humphrey Lyttelton had been told they couldn’t perform the tour commercially because the corporation owned the rights.
However, after Cryer spoke out about his disappointment, the corporation has now struck a deal to allow the show on the road.
A Radio 4 spokesman said: ‘We're pleased to confirm that the I'm Sorry I Haven't a Clue team are able to go on tour under the banner of the Clue name.
‘We have been talking about how to make this happen for some time and are delighted at the positive result.’
Cryer had accused the corporation of being 'bloody stingy' about the proposed tour.
The few radio recordings each year are an instant sell-out - and the team can now expect to sell thousands of tickets to live shows.
