The 25-year-old shooter, who holds the world record, scored 188 points, beating Hakan Dahlby of Sweden, who claimed silver with 186 points.
Vasily Mosin of Russia won the bronze medal after winning a shootout with Fehaid al-Deehani of Kuwait. The two were tied at 185.
"It was an emotional roller coaster for me from start to finish," Wilson said after scoring 188 out of 200 shots fired.
The No. 2 ranked Briton was on target during three qualifying rounds, scoring 143 out of 150 points to reach the finals at the Royal Artillery Barracks with a three-point lead ahead of Mosin. Although Wilson maintained a consistent lead, he felt the pressure halfway through the finals, missing five targets — including a double — as Mosin narrowed the lead to one point.
"I did know that Vasily got quite close in the middle and then I got further ahead at the end. But dropping a complete pair was not in the plan," Wilson said.
Some shooters appeared to have struggled with the wind Thursday. Top-ranked Joshua Richmond of the United States missed six targets during the qualifying round of the medium-range event and finished in 17th place.
"Today was one of my toughest days ever," Richmond said. He had struggled with his holding points and missed a lot more first targets.
"I was somewhat chasing my tail all day trying to figure it out and put a run together," Richmond said, adding that total of 133 points was disappointing.
"The score wasn't the one I was looking for," Richmond said.
Beijing gold medallist Glenn Eller of the U.S. also missed the final after finishing 22nd with 126 points.
"Unfortunately, I got behind early and basically chased my tail until I was out of it," Eller said.
Mosin, who aimed for the gold, was disappointed with his performance with which he claimed the bronze in double trap shooting, where two clay targets are released simultaneously.
"The wind is nothing in an Olympic competition. Nothing. It's all mental," Mosin said. The reason he failed to overcome Wilson despite trailing him by a point was because he did not keep the shooting simple, he said.
"You set to do your normal job, and then you try to do it a little bit better. This is the main mistake," he said. "You have to do your job. Boom, boom and boom, boom, and nothing more."
Everything was as it should for Dahlby, the silver medallist .
"It was one target at the time and that's what double trap is," Dahlby said.
The last British gold medal in the event was won by Richard Faulds in the 2000 Sydney Games. The 35-year-old Faulds was competing on Thursday during his fifth Olympic appearance. He finished 12th with a total of 133 points.