The heavyweight made short work of the Italian, knocking him out in the first round, with Leo needing an oxygen mask to help him recover afterwards.
"Winning the Olympics was a priceless experience as well and this is my pro debut, there's only one pro debut and we ended it in spectacular fashion," Joshua is quoted as saying in the Daily Mail.
"It's just a start though, I don't want to get carried away, it's just the beginning but we can build on that and that's the main thing.
"Every time I step into the ring is as important as an Olympic final. I've got to take my career serious. I felt good and relaxed. If this is what I can do after 14 months out of the ring, let's see what I can do after another 14 months in the ring."
Joshua had not fought since winning Olympic Gold last year, prior to the win over Leo.