Team-mate Kristian Thomas posted 15.0 early on in Switzerland but was beaten into second when Wilson scored 15.3 on the last routine.
City of Leeds gymnast Wilson, 20, said: “That feeling was incredible.
“You train your whole life for moments like that standing on the top of podium singing the national anthem with a gold medal.”
On Saturday, GB won silver in the team final in Bern behind Russia and ahead of the hosts Switzerland.
Wilson and Thomas had scored 15.033 to go through to the high bar final as joint-best qualifiers.
Thomas, up second, had watched several gymnasts stutter before Wilson came through at the end to snatch gold with a near-flawless routine.
Wilson added: “All the better to do it alongside Kristian, who’s helped me so much the last two years on the senior circuit.
“I’d hit that routine twice very well this week so I knew I could do it.
“I felt the nerves today, definitely, but I got through it and I can’t be happier.”
For Thomas, it was a happier ending to a frustrating day having finished fourth earlier in both floor and vault finals.
Thomas was gracious in praising his team-mate despite being toppled off the gold medal perch at the very last.
“It’s a great way to end the event personally and for GB,” Wolverhampton-born Thomas, 27, said.
“Nile deserves huge credit to go last out and produce a routine like that.
“I’ve had a brilliant week. It’s been all about consistency and proving the kind of form I’m in and to then end with a silver medal on the podium with a team-mate is perfect.”
There was an uncharacteristic error from Louis Smith on the pommel as the world silver medallist’s hand slipped and he fell off the apparatus to also finish fourth.
In other finals, Courtney Tulloch gave another fine showing on rings to come joint fourth, while Dan Purvis was eighth on the floor.
The event is the last major competition before the Rio Olympics team selection is announced on July 12.