On 8 May 1946, a memorial fire was lit on Piłsudski Square in Warsaw in memory of those killed in the recently-ended war. The eternal flame became part of the restored “Tomb of the Unknown Soldier” memorial. The memorial had been created before the war, but was badly damaged during the German occupation of Warsaw.

The honour of lighting the flame was given to the Divisional General and Mayor of Warsaw, Marian Spychalski. An honour guard of the Polish Armed Forces Representative Regiment was stationed at the memorial.

The tradition of lighting a flame in honour of fallen soldiers has existed since ancient times.  In more recent memory, the first eternal flame was lit in 1923 at the Arc de Triomphe in Paris. Later, eternal flame memorials appeared in Belgium, Portugal, Romania, and the Czech Republic.

The first eternal flame in the Soviet Union was lit in October 1957 in Leningrad on the Field of Mars at the Monument to the Fighters of the Revolution. The eternal flame on the Field of Mars was the source of the flames for most of the military memorials established in the hero cities of the USSR.

On 8 May 1967, the eternal flame in memory of those killed in the Great Patriotic War was lit in  the Alexander Gardens near the Kremlin wall in Moscow.

Source: 

The Eternal Flame in Russia and the World: History of the Tradition. RIA Novosti