Veselý improved his personal best by more than five metres at a meeting in Olomouc in May 2010, throwing a world leading mark of 86.45 m. He was ninth at the 2010 European Athletics Championships that year. He came close to a major medal with a fourth-place finish at the 2011 World Championships in Athletics. He had his second best ever throw at the Shanghai 2012 Diamond League meet, winning with a mark of 85.40 m. At the 2012 Olympic Games, Veselý threw a new personal best of 88.34 m to improve his world lead; in the final, however, his last throw of 83.34 m was only good enough for 4th place. In 2017, following the disqualification of Oleksandr Pyatnytsya due to doping, Veselý was awarded the bronze medal.