Storck made his player debut in the Bundesliga with VfL Bochum. In the summer of 1983, he moved to Borussia Dortmund, where he remained for six years. His biggest success as a pro was winning the 1988–89 DFB-Pokal. He played in 170 Bundesliga matches and scored eight goals.
At the same time he has also managed Kazakhstan national under-21 football team. Storck has complained about the state of the Kazakhstan Premier League and the lack of cooperation he encountered from the local clubs' management. On 1 March 2010, Storck signed a new one-year contract as coach of Kazakhstan national football team. Viktor Katkov, vice-president of Football Federation of Kazakhstan, said that "Our young team are progressing with every match, as shown by the games against Croatia and Ukraine at the end of 2010 FIFA World Cup qualifying. Bernd's football philosophy is a modern one and we are sure it will promote further improvement." Storck added: "I am proud to have the opportunity to continue my work with the Football Federation of Kazakhstan. We have made progress and I am keen to continue working with the team. It is interesting for me to see young footballers develop, and the whole of Kazakh football is developing right now and its status in Europe improving. I hope our work together will bear fruit and that the team can do well for the fans in EURO 2012 qualifying." He was sacked on 16 October 2010 after a poor start to Euro 2012 Qualifying. Kazakhstan lost to Turkey, Austria, Belgium. His final game was a 3-0 defeat against Germany. Sayan Khamitzhanov, general secretary of the Football Federation of Kazakhstan said that "We can see the team progressing because young players are gaining important experience. However, he had a task to collect at least three points in four matches and that was not done. That is why the federation has decided to turn to another coach."
On 20 July 2015, he was appointed as the head coach of the Hungary national football team after the resignation of Pál Dárdai who became the manager of the Bundesliga club, Hertha BSC. On 4 September 2015, Hungary drew with Romania at the Groupama Arena, and three days later on 7 September 2015 Hungary drew with Northern Ireland at the Windsor Park, in Belfast, Northern Ireland. On 20 October 2015, Storck fired the assistant coaches of the Hungary national football team including Imre Szabics, István Sallói, József Andrusch. Storck convinced his former teammate, Andreas Möller, to help him preparing the national team against Norway in the UEFA Euro 2016 qualifying play-offs. On 15 November 2015, Storck-led Hungary qualified for the UEFA Euro 2016 after 44 years when Hungary was qualified for the UEFA Euro 1972. Hungary beat Norway in the first leg of the UEFA Euro 2016 qualifying play-offs 1-0. The only goal was scored by László Kleinheisler, who had not played a single match in the 2015–16 season in his club Videoton. On the return match, Storck's team beat Norway 2-1 and qualified for the UEFA Euro 2016 finals. One day after the successful playoff match against Norway, Stork extended his contract with the Hungarian Football Federation until the end of the UEFA Euro 2016. In an interview with the Hertha BSC's official website, Pál Dárdai, former head coach of Hungary, said that he built the base of the team, while Storck added his part to reach the finals of the UEFA Euro 2016. In an interview with the Hungarian Nemzeti Sport, Storck was asked what his best decisions were since his appointment. He said that he would have liked to attack against Romania in the UEFA Euro 2016 qualifying Group F match at the Groupama Arena, Budapest, to show his philosophy but he decided to defend because he did not have enough time before the match to rebuild the team. He also pointed out that the fact that he had nominated both Gábor Király and Richárd Guzmics in the starting line-up had been a good decision. On 14 June 2016, he managed Hungary in the first group match in a 2–0 victory over Austria at the UEFA Euro 2016 Group F match at Nouveau Stade de Bordeaux, Bordeaux, France. Three days later on 18 June 2016 his team drew with Iceland at the Stade Vélodrome, Marseille. In the last group match Hungary drew with Portugal at the Parc Olympique Lyonnais, Lyon on 22 June 2016. On 15 June 2017, he offered his resignation after a shocking 1–0 defeat against Andorra in the 2018 FIFA World Cup qualification match. However, the director of the Hungarian Football Federation did not accept his resignation, therefore Storck was confirmed in his position and was a given another opportunity to gain more points during the qualification process. On 17 October 2017, he lost his job in Hungary with mutual agreement.
