The Ukrainian gymnast scored 15,399 for his two attempts on the vault, leaving behind Artur Davtyan from Armenia and Marian Dragulescu from Romania (both sharing 15.316 points).
Verniaiev came second on the parallel bars, scoring 15,716 points. Russian David Belyavsky obtained the gold medal (16,033).
Ukraine took the 4th place in the team competition and won no medal. The European Championships took place in Bern from 25 to 29 May.
Earlier Verniaiev won parallel bars after winning floor exercise and pommel horse at the Varna World Challenge Cup in Bulgaria.
Oleh Verniaiev represented Ukraine at the 2012 Summer Olympics where he finished fourth with the team and eleventh in the all-around. He is the 2014 World Champion and 2014 European Champion on the parallel bars. At the 2015 European Artistic Gymnastics Championships Verniaiev won the Individual All Around. At the 2015 European Games, Verniaiev was part of the Ukrainian team, winning silver in the Team Final behind Russia.
Watch his performance in footage from GutsuFan below: