Walden, 33, is a writer and the daughter of British politician George Walden.
Morgan, who judges Britain's Got Talent and America's Got Talent, did not invite fellow reality show judge Simon Cowell:
And he kept the ceremony free of showbiz glamour with just a handful of family and friends on the guestlist, with no sign of fellow BGT judges Simon Cowell or Amanda Holden.
When asked why he had not asked Simon to be best man, Piers said: 'I couldn't trust him to turn up on time. He's terrible at timekeeping.'
But, as usual, Simon managed to have the last word.
He said: 'I hate to admit it but I'm absolutely thrilled for the two of them. Having met Celia, I have no idea how he managed to pull this one off.'