Born in Sofia, Bozhkov first started to play for a local team Sportist Hadzhi Dimitar. He made his debut on 20 September 1938, on his 15th birthday, in a game against Fortuna. During his club career he played for PFC CSKA Sofia. Bozhkov won the top Bulgarian league, the A PFG, a ten times (all with CSKA), as well as the Bulgarian Cup, three times (all with CSKA). He earned 53 caps and scored 4 goals for the Bulgaria national football team from 1946 to 1958, and won a bronze medal at the 1956 Summer Olympics. He later coached the national team in the 1970 FIFA World Cup and won a silver medal at the 1968 Summer Olympics.