The 25-year-old led from start to finish at the Royal Artillery Barracks.
Wilson, the world record-holder and world number two in the event, was three points ahead going into this afternoon's final after three qualifying rounds in the morning.
And in a tense final shoot-out Wilson missed five shots, including a double as he closed in on gold.
He smashed the world record in Arizona in March, scoring an incredible 198, and is now Britain's first Shooting medallist since Richard Faulds won gold in the same event in Sydney 12 years ago.
Wilson needed one hit from the final two targets but got both before falling to his knees in tears.
A capacity crowd gave the new Olympic Games champion a standing ovation before he climbed into the first row of seats to greet his mother and tearful girlfriend.
As he was surrounded by photographers he simply said: 'It's awesome, fantastic.'
Dahlby took silver while, behind the celebrations, Russian Vasily Mosin won bronze after a shoot-off with Kuwaiti Fehaid Aldeehani.