Prominent atheist Prof Dawkins and the former Archbishop of Canterbury will discuss whether "religion has no place in the 21st Century" on Thursday.
They were involved in a public discussion at Oxford University last year.
Ben Kentish, president of the union, said it should be a highlight of the debating society's 200-year history.
"Our speakers are the most renowned commentators on this subject," he said.
In Cambridge, about 1,000 students will be in the audience.