This period in galactic history was predicted by the Organian race when they imposed a peace between the United Federation of Planets and the Klingon Empire. The transcended race believed that, in time, the two empires would become friends and allies in the future.
During the tense period of cold war between the Empire and the Federation, the Klingons orchestrated an elaborate ruse where they tricked James T. Kirk into believing he had been accidentally sent a hundred years into the future where the Great Peace had occurred thanks to the New Klingons. This was actually a plot in order to allow the Klingons to sneak a fleet to Earth and destroy the leadership of the Federation but Kirk managed to thwart the plan. (TOS novel: Timetrap)