From 1976 to 1987, Tkachenko played on the senior men's Soviet Union national basketball team, participating in many FIBA EuroBasket and FIBA World Cup competitions. With the Soviet national team, he won numerous medals, including: two bronze medals at the 1976 Summer Olympic Games and at the 1980 Summer Olympic Games, the gold medal at the 1982 FIBA World Championship (also silver medals at the 1978 FIBA World Championship and the 1986 FIBA World Championship); as well as three gold medals at the FIBA EuroBasket: at the FIBA EuroBasket 1979, the FIBA EuroBasket 1981, and the FIBA EuroBasket 1985 (also silvers at the FIBA EuroBasket 1977 and the FIBA EuroBasket 1987).