Ievgen Budnik was born on September 4, 1990 in the city of Lutsk. He started playing football at the age of 7, attending the football school of FC Arsenal Kharkiv, where for three years in a row (2006, 2007, 2008) Budnik was recognized as the top-scorer. The first professional team of the striker was FC Arsenal Kharkiv, playing in the Second League of Ukraine. In the 2010/11 season, Budnik moved to Metalist Kharkiv, which at that time played in the Premier League of Ukraine. After that, the Ukrainian striker defended the colors of FC Vorskla Poltava for a long time. In the 2013/14 season, Budnik moved to the Czech club Slovan Liberec, after spending two seasons there, the player returned to Vorskla again.

Throughout his career, Budnik played in such clubs as Stal Kamianske, Dinamo Minsk, Austrian Kapfenberger SV, in the Greek clubs Platanias FC and PAS Lamia 1964, as well as in the Estonian club FCI Levadia Tallinn.

In the summer of 2019, Ievgen Budnik joined Urartu Football Club. The forward spends half a season in the Yerevan club, taking part in 11 matches and scoring 4 goals. During the 2020 winter transfer window, the Ukrainian striker moves to the Indonesian football club Persita Tangerang FC. However, exactly a year later, Budnik returned to Urartu FC.

Ievgen Budnik was also invited to the national teams of Ukraine U-20 and U-21.