The tour will open at the Grand Theatre in Leeds on 23 July 2014 followed by dates in Bristol, Nottingham, Belfast, Dublin, Oxford, Manchester, Aberdeen, Canterbury, Newcastle, Glasgow and Sheffield.
Further venues are still to be announced.
Originally directed (in the West End) by Jason Moore and Rob Ashford, the show is based on the story and characters from William Steig's book Shrek! and the Oscar-winning DreamWorks Animations film.
DreamWorks' Bill Damaschke said: "We are thrilled that Shrek and his fairy-tale friends will be heading out on tour across the UK and Ireland and delighted that our very own Nigel Harman will be directing.
"It has been such a joy to bring this loved story to life and we can't wait for families up and down the country to experience their beloved swamp-dwelling ogre, Princess Fiona, Donkey and all their pals live on stage, as so many have on Broadway and in the west end."
Harman, who won a WhatsOnStage and Olivier Award for his portrayal of Lord Farquaad, added: "I am delighted to be returning to Shrek as its director. This show is very special to me with its dizzying blend of great characters, a hilarious script and sublime music... In short, there was no way I was going to say no to the challenge of realising the production for the UK and Ireland."