Dobrev started training weightlifting in 1991 under the coach Georgi Yotovski, when he was in sixth grade at the Vasil Levski Sports School and competed for the team of Maritsa.

Later in 2001 he also made a debut at the 2001 World Championship in Antalya, Turkey, winning his first total bronze medal in the 85 kg category.

The following year in Doha, Qatar, he managed for bronze at the World Championships, which accounted for his last eight medal on a senior level.

Milen Dobrev collected 4 gold, 2 silver and 2 bronze medals out of 10 major senior competitions in which he took part throughout his career.

On April 20, 2005, at a ceremony in the Greek Embassy in Sofia, Bulgaria, he was also named honorary citizen of Athens, Greece.