Vernyayev was born in Donetsk. He was educated at the Donetsk State Institute of Health, Physical Education and Sport. Vernyayev resides in Kiev. He is coached by Gennady Sartynsky.
Vernyayev finished 6th in the 2012 American Cup with a score of 88.132. At the 2012 European Men's Artistic Gymnastics Championships he participated in the team all-around final for the Ukrainian team that finished in 5th. He also made the parallel bars final, finishing in 2nd place with a score of 15.66, 0.1 points behind the winner Marcel Nguyen. He was victorious in the all-around final of the Ukrainian Championships, scoring 90.300 points and winning by a margin of 2.65 points over 2nd place Oleg Stepko. Vernyayev competed for the national team at the 2012 Summer Olympics in the men's artistic team all-around, alongside Nikolai Kuksenkov, Vitalii Nakonechnyi, Oleg Stepko and Igor Radivilov, and the men's artistic individual all-around. In qualification he scored 88.964 to finish in 13th place. In the team final Ukraine finished in 4th with a score of 271.526, missing out on a medal by less than 0.2 points. Ukraine were initially awarded 3rd place for a bronze medal, however following an appeal from Japan over a pommel horse score, they were awarded an extra 0.7 points, allowing them to move from 4th place to 2nd knocking Ukraine out of the medals in the process. He finished in 11th place in the individual all-around final with a score of 88.931.
2013
Vernyayev won the Ukrainian National Championships. He took the silver medal in individual all-around at the 2013 American Cup. He then won the bronze medal in all-around at the 2013 European Championships in Moscow, Russia. At the 2013 Summer Universiade, Vernyayev led his Ukrainian team to a second-place finish in the team final and qualified for the all-around final. He won the all-around bronze medal. He won another bronze medal in the parallel bars final.
2014
In May 2014, at the 2014 European Championships in Sofia, Vernyayev contributed scores of 15.100, pommel horse, rings, vault, 15.591 and 14.600, helping Ukraine win the team bronze medal with a total score of 262.087 points behind Great Britain. In event finals, Vernyayev won the gold in parallel bars and won bronze medal in vault. He won gold in parallel bars at the 2014 World Championships in Nanning. After the wrong anthem was played during the medal ceremony, he said "It was written in my face that I didn't like it. They came up and apologised for the anthem and promised to change it for TV broadcast. But I thought it would be incorrect, because I screwed up my face and it will be even worse if the anthem is replaced."
2015
In March Vernyayev won the American Cup in Arlington, Texas. He won with a score of 90.597, 0.499 over silver medalist and 2013 World Championships all-around silver medalist Ryōhei Katō of Japan. Vernyayev also became the FIG World Cup series champion as well in addition of winning the American Cup. At the 2015 European Artistic Gymnastics Championships Vernyayev won the individual all-around with a score of 89.582, beating 2013 champion David Belyavskiy. He also qualified to the parallel bars final where he won the gold medal with a score of 15.866. At the 2015 European Games, Vernyayev was part of the Ukrainian team, winning silver in the team final behind Russia. Vernyayev qualified into the all-around, floor, pommel horse, vault, parallel bars and high bar finals. He won the all-around final with a score of 90.332, and the vault final with a score of 15.266. He placed 6th in the floor final with 14.233, and 5th on pommel horse, parallel bars and high bar.
2016
At the 2016 European Championships, Vernyayev won a gold medal on vault and a silver medal on parallel bars. In August 2016, Vernyayev claimed silver in the men's all-around competition at the Rio Olympics with a score of 92.266, only 0.099 behind Kōhei Uchimura's 92.365. This was the closest anyone had scored to Uchimura since 2008. It was considered by many the best all-around duel in men's gymnastics history. Vernyayev also gained prominence due to his public apology over the Ukrainian team's behavior during the team competition. Vernyayev won the gold medal in the parallel bar competition, scoring 16.041, and finished 5th in the vault final and 8th on pommel horse and the horizontal bar. It was Ukraine's first gymnastics gold at the Games 2004. His all-around medal was also Ukraine's first since the bronze of Alexander Beresch at the 2000 Games.
2017
At the 2017 European Championships, Vernyayev won gold medals in the individual all-around and parallel bars and a bronze medal on vault. At the 2017 Taipei Summer Universiade, Vernyayev won the gold medal of individual all-around, three silver medals on team, vault, and pommel horse, and one bronze medal for ring.
