Wilson said: "That feeling is just incredible. To be standing there with our team captain Kristian, someone who has helped me so much and is such a great role model, makes it even more special.
"I felt the nerves before my routine but had to stay focused, I knew I had it in me and I did it. We move forward to focus on Rio now," he added.
Russia's David Belyavskiy was third and took gold in the parallel bars with a score of 16.033 ahead of Ukraine's former world champion Oleg Verniaiev, on 15.716, who also took the vault with 15.399.
Belyavskiy claimed his third medal, a silver behind Armenia's Harutyun Merdinyan on the pommel horse, after favourite Louis Smith of Britain, the world silver medallist, slipped and fell. Smith finished fourth.
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Greece's world champion Eleftherios Petrounias (15.866) retained his European title on the rings.
Nikita Nagornyy completed a successful championships for Russia, who took the team gold on Saturday, by winning the floor exercise in 15.566 ahead of Romania's Marian Dragulescu.
(Writing by Neil Robinson in London; editing by Clare Fallon)
