Heydarov broke into the judo elite in 2017. He won the European Championship at the age of 20, the first of his four titles. In the following two years, he won two bronze medals at the World Championships. However, he didn't make it to the Tokyo 2020 Olympics because he was behind his compatriot, Rio 2016 silver medallist Rustam Orujov. 

After Tokyo 2020, where Orujov finished fifth, Heydarov established himself as Azerbaijan's number one in the -73 kg category. Orujov retired in 2023, leaving Heydarov as the only candidate for Azerbaijan at Paris 2024.

Heydarov won 3 consecutive European titles from 2022-2024. He also won several IJF Grand Slam titles and another bronze medal at the 2022 World Championships. Despite being the world leader in his weight category, Heydarov couldn't win the world title each time.

The breakthrough came in 2024, when Heydarov finally won gold at the World Championships in Abu Dhabi and went on to become Olympic champion in France.

"There are a number of tournaments ahead, as well as the Summer Olympic Games to be held in Los Angeles in 2028. My goal is to win a gold medal in this competition. If you have self-confidence in the competition you will participate in, success will be with you," Heydarov told reporters at the Heydar Aliyev International Airport, Azernews reports.

Heydarov defeated France's Joan-Benjamin Gaba in the final of the Paris 2024 Olympics to become Olympic champion. Azerbaijan won two gold medals in Paris after Zelym Kotsoiev won the -100kg category.