[5] At the 2011 World Championships he competed in the team all-around event with Nikolai Kuksenkov, Vitaliy Nakonechnyi, Oleg Stepko, Igor Radivilov, and Roman Zozulya, finishing in fifth.

He also made the parallel bars final, finishing in second place with a score of 15.66, 0.1 points behind the winner Marcel Nguyen of Germany.

[9] Verniaiev competed at the 2012 Olympic Games in the men's team event alongside Nikolai Kuksenkov, Vitalii Nakonechnyi, Oleg Stepko and Igor Radivilov.

Ukraine was initially awarded third place for a bronze medal; however following an appeal from Japan over a pommel horse score, the Japanese team was awarded an extra 0.7 points, allowing them to move from fourth place to second, knocking Ukraine out of the medals in the process.

In May 2014, at the 2014 European Championships in Sofia, Bulgaria, Verniaiev contributed scores of 15.100 (floor), 14.400 (pommel horse), 14.900 (rings), 14.783 (vault), 15.591 (parallel bars), and 14.600 (horizontal bar), helping Ukraine win the team bronze medal with a total score of 262.087 points behind Great Britain.

At the 2015 European Championships Verniaiev won the individual all-around with a score of 89.582, beating 2013 champion David Belyavskiy.

In August 2016, at the 2016 Olympic Games, he won the silver medal in the men's all-around competition with a score of 92.266, only 0.099 behind Kōhei Uchimura's 92.365.

In 2019 Verniaiev competed at the European Championships where he placed seventh on pommel horse and eighth on parallel bars.

He next competed at the 2019 European Games where he won gold on parallel bars, silver in the all-around and on pommel horse, both behind David Belyavskiy.

In December 2020 Verniaiev was notified by the International Gymnastics Federation that he was provisionally suspended from competition, backdated to November 2020.

The reason for the suspension was a positive test for meldonium, which was banned by the World Anti-Doping Agency starting in January 2016.

In July 2021 Verniaiev expressed his intention to appeal the suspension to the Court of Arbitration for Sport, contending that meldonium was not found in subsequent tests.

[17] On March 14, 2023, Verniaiev announced that his appeal was successful and the CAS reduced his ban to two years, resulting in his ability to return to competition immediately.

[18] Verniaiev made his return to competition in September 2023 at the Mersin Challenge Cup where he won gold on parallel bars and silver on pommel horse behind Ahmad Abu Al-Soud.