Savichev was born on February 13, 1965. He made his mark as a player of Torpedo Moscow, scoring 47 goals between 1984 - 1990. He came to Greece and Olympiakos in 1990. In the next two seasons he scored 17 goals for the Piraeus outfit.
Following his stint at Olympiakos, Savichev played in Germany for Saarbruecken and St Pauli before retiring in 1999.
Savichev holds the distinction of having scored the winning goal, in extra time, in the final of the 1988 Olympic Games, giving the USSR a 2-1 victory over Brazil.
His career in Greece