The 21-year-old carded a two-over-par 74 on Thursday to leave his weekend participation in doubt, only to bounce back with a stunning 67 to extend his stay at St Andrews.
Successive 71s over the weekend took the European Amateur champion to five-under-par, six shots clear of his nearest challenger Aaron Jarvis, with his Championship coming to a fitting conclusion when he birdied the 18th in front of his beaming parents greenside.
Celli also had an eagle to celebrate on Sunday, a superb approach at the par-5 14th setting up a routine putt that all but sealed the Silver Medal for the Italian.
The youngster outlined his Ryder Cup ambitions after his round on Saturday, with Rome to host the battle between Europe and the USA next year, and will feel he has the world at his feet after outscoring some global greats on the Old Course.
Dream Moment for Celli
"It is unbelievable and an unforgettable moment," he said. "It is a dream come true just to play here, so to win the Silver Medal is amazing.
"I was a little bit upset because I had made a bogey at 17 but I wanted to enjoy the moment as it is amazing to walk up the 18th at St Andrews.
"Today my golf game was really good, like the last three days. And today I made a lot of stupid bogeys, I can say that.
"But that's okay, because I'm very happy because my dream was to play here, and I also won the Silver Medal. I can't ask for a better thing to win the Silver Medal at The 150th Open in St Andrews."