Varnyú started the World Cup for the first time in Moscow in February 2012 and finished 35th over 1500 m and 33rd place over 1000 m. At the 2014 Junior World Championships in Erzurum , he won the silver medal with the relay. In March 2018, he finished eighth in the relay at the World Championships in Montreal . In the 2018/19 season he won his first World Cup victory in Salt Lake City with the relay and took third place with the relay in Dresden . He also achieved his first top ten placement in the World Cup singles in Salt Lake City with eighth place over 1000 m. At the 2019 European Championships in Dordrecht , he won the gold medal with the relay. In March 2019 he won the bronze medal with the relay at the World Championships in Sofia . In the all-around competition he achieved 33rd place there.