In 2015, he won the triple jump competition at 2015 European Games in Baku. A month later, Babayev set a championship record, national junior record and world junior lead when he leapeed 17.04m in the triple jump at 2015 European Athletics Junior Championships. Babayev competed in the 2016 Summer Olympics in Rio and the 2020 Summer Olympics in Tokyo, competing in the Men's triple jump.