The two-parter, which is being done in aid of Stand Up to Cancer, will see five contestants paired up with a comic to train them in the art of stand-up, before one is crowned champion.
Also taking part are broadcaster and former Strictly Come Dancing contestant Reverend Richard Coles, Happy Mondays frontman and I'm a Celebrity star Shaun Ryder, and former Conservative party co-chairwoman Baroness Sayeeda Warsi.
Curtis will be coached by Judi Love, while Katie will get guidance from Zoe Lyons. Meanwhile, David Baddiel will coach Richard, Jason Manford will guide Shaun, and Sayeeda will get her teachings from Nick Helm.
"This joyous Fact Ent series is both a masterclass in comedy, and a dramatic test of character," said Becky Cadman, commissioning editor for factual entertainment at Channel 4.
"A Reverend, an actress, a politician, a reality star, and a musical legend already sounds like the start of a joke, and watching them learn the craft of stand-up from five of the best in the business is brilliantly entertaining."
Sarah Tyekiff, head of unscripted series at Lime Pictures, added: "Lime Pictures are excited to kick off 2021 with some unexpected one liners and a lot of laughs, with this fantastic Fact Ent series for Channel 4 and Stand Up to Cancer.
"Stand Up and Deliver has been an unforgettable format to make. With some of the UK's biggest comedy names leading the way, it's full of surprises, shocks and sheer fear as, for one night only, five brave celebrities battle it out for the biggest laughs."
Meanwhile, Curtis recently responded to his brother AJ entering the current series of I'm a Celebrity, admitting he will be voting for him "to do as many trials as possible".
Stand Up and Deliver will air on Channel 4 as part of Stand Up to Cancer 2021.
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