Leonyuk was born in Minsk, the capital of the Byelorussian Soviet Socialist Republic, modern day Belarus.

He lost in the first round of the singles to Ramesh Krishnan and also played in the doubles draw with Igor Tihonenko.

[3] A regular Davis Cup representative for the Soviet Union, he appeared in 13 ties in the 1980s, including stints in the World Group.

In 1985 he and Alexander Zverev came from two sets down to win a doubles match over Czechoslovakia's Tomáš Šmíd and Libor Pimek in Tbilisi.

In the wake of the Chernobyl disaster, Leonyuk moved to Brooklyn, New York to ensure his children's safety.