Born in the village of Stambolovo in the southwestern part of Bulgaria, Velichkov started his active sports career in sixth grade, when he joined the local cross-country skiing club. He later switched to biathlon. Velichkov participated in his first Olympics in 1980 and he debuted at the World Championship-level at the World Championships in Minsk in 1982. He also participated in the Olympics in 1984 and 1988 and the World Championships in 1983, 1985, 1986, 1987, 1989 and 1990 for Bulgaria. His best individual finish at the Olympics came in the 20 km individual in 1984, he finished 13th. His best, and only, relay finish came in 1988, an 8th place. His best individual finish at the World Championships came in 1982 in Minsk where Velichkov finished 5th, a feat he copied three years later in Ruhpolding, both in the sprint. His best relay finish at the World Championships was a 10th which came in 1989 in Feistritz, where his best, and only, team event finish also came, a 12th place.