The Golden Snitch was introduced into Quidditch in the year 1269 C.E., as the magical bird The Golden Snidget.
The story goes that at a Quidditch Game in said year, Barberus Bragge, who was Chief of the Wizard's Council (Ancient Equivalent of the Minister of Magic) offered a 150 Galleon (now worth more than a million galleons) prize to the player who caught a golden snidget during the match. Bragge released the Snidget from a cage which he brought along. However, the Snidget was rescued by a sympathetic bystander.
After that, matches ended as they do now, with the catching of the Golden Snidget.
Eventually, the Golden Snidget neared extinction, so a substitute was needed. The Golden Snitch was invented by Metal-charmer Bowman Wright of Godric's Hollow.
Some information (translated into my own words) was taken from Quidditch through the ages
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