Leonenko began his career with stints at Russian clubs such as Geolog Tyumen and FC Dynamo Moscow, before transferring to FC Dynamo Kyiv in 1992, where he played until 1998. A successful forward for Dynamo in the early to mid 1990s – Leonenko was named Ukrainian Footballer of the Year in 1992, 1993, and 1994 – Leonenko was eventually forced to the bench with the emergence of the striker partnership of Serhiy Rebrov and Andriy Shevchenko. In 1998, he moved to play for CSKA Kyiv and ended his career with FC Zakarpattia Uzhhorod in 2001.

Born in Russia, Leonenko chose to play for the Ukraine soon after transferring to Dynamo Kyiv. During his four years representing the Ukraine from 1992 until 1996, Leonenko earned 14 caps and scored 6 goals.