Tkachenko, a 7 ft 3 in (2.21 m), 310 lb (140 kg) center, was a great defensive player. He could block out 2-3 opponents to give teammates a chance to grab a rebound. His offensive ability was important, too, as his post up moves were basic but effective and his shooting was good for a player of his size, with a range of approximately 17 feet.
Tkachenko began playing for Stroitel Kiev in the 1973-74 season, when he was 16 years old. He continued to play for them through the 1980-81 season. In 1983, he began playing for CSKA Moscow and he stayed there until his retirement after the 1988-89 season.