Zhekov was born in Knizhovnik, Haskovo Province, and began his career at F.C. Dimitrovgrad. He was initially deployed as a defender, but on the advice of manager Hristo Hadzhiev switched to the forward position. Later he moved to Beroe Stara Zagora, where he twice became Bulgaria's top goalscorer. Between 1968 and 1975 Zhekov played for CSKA Sofia and scored 144 goals for the team. This makes him the club's best goalscorer of all time. He also won the European Golden Boot in 1969 and two European Bronze Boots. He has 333 appearances and a record of 253 goals in the Bulgarian A Group.