The 22-year-old welterweight will fight at the SSE Arena on the undercard of Ricky Burns' super-lightweight unification bout with Julius Indongo.
He lost to eventual champion Daniyar Yeleussinov of Kazakhstan in round two of last year's Olympics in Rio.
"The pro game will suit me, I'm business-like and I think I can sell myself," said Kelly, from Sunderland.
"I want to get fans across the whole of Britain and beyond to want to watch me and come to my fights. I think they'll see flash and flair, and there will be KOs too."
He has signed with promoter Eddie Hearn and will be trained by Adam Booth - former trainer of David Haye - who also currently oversees WBO middleweight champion Billy Joe Saunders.
Kelly added: "My style is perfect for Adam, he loves flair but he knows how to control it. He lets you express yourself but he doesn't neglect the basics."
British Olympian Josh Kelly will make his professional debut in Glasgow on 15 April, against an unnamed opponent.