The world record holder shot 188 out of 200 to win gold ahead of Sweden's Hakan Dahlby in second on 186 in front of a capacity crowd at the Royal Artillery Barracks in south east London.
Russia's Vasily Mosin took bronze after a shootoff with Kuwait's Fehaid Aldeehani as both finished on 185.
Wilson had looked assured in taking a three point lead into the final after topping qualifying with a score of 143 out of 150.
He never lost his lead throughout the 50-shot final, where he was cheered loudly by the partisan crowd every time he brought pink smoke from the orange clays.
However, Wilson missed both clays in the 21st round of the final as Dahlby, who hit 49 of 50 targets, closed but the Briton hung on and finished in style by hitting the final two clays.
“What a feeling – what a rush,” he said.
“The gold medal meant a huge amount to me. It’s really difficult – I’ve watched us in the past and I’ve watched us win medals.
“You watch these guys after they’ve won them and they say that it’s impossible to talk about it, but it really is.
“It was an emotional roller coaster for me from start to finish. There’s a lot of people I have to thank, but most of all my coach [and Athens 2004 gold medallist] Ahmed Al Maktoum. Without him, I wouldn’t be here.”
Wilson held his own in the final round after having a clear lead, but it was a worrying last few shots for the Brit, who afforded himself one eye on the scoreboard.
He said: “I thought to myself that I’d allow myself a look at the board on the fourth pair.
“When they came around, I missed the pair. I kept going – I came in with a lead and there was a possibility.
“I realised I needed to shoot the rest and what a feeling. I really don’t know what to say – I’m an Olympic gold medallist, what a weird thing to say.”