This notion is as old as the idea of progress. Condorcet painted a development of human society from "savagery" to something that has yet to be achieved. Hegel believed there was a "world-spirit" which caused humans to criticize their present conditions and refurnish them according to their ever new ideas of propriety. Eventually, Hegel claimed, "history" would end and we'd get a "Kingdom-of-Heavens-On-Earth". Marx believed that it was the economy and not some "world-spirit" that was the "motor of history". Kant already claimed there could be no wars in a Democracy (in "Zum Ewigen Frieden") but since the parliament, to Marx, was "but a committee for managing the common affairs of the whole bourgeoisie" he postponed this eternal peace until you got Communism with it's direct democracy, no class divisions and common ownership on the means of production. Fukuyama is not the first one to have claimed we have achieved this end of history either. There were a plenty of Hegelians who would claim their particular state is, in fact, the veritable kingdom of heavens on the earth.

Edit: of course, Fukuyama does not believe we have really achieved it just yet. It has just been achieved in the West and now must be exported into the rest of the world. This approach is very reminiscent of pre-Stalinist Bolshevism. Trotsky planned to export his end of history into Germany and into India.

This is more a question for /r/Ask_Politics than here. Its been ages since I had to study Fukuyama, but my understanding is that by History he doesn't mean the end of new events or anything, but the end of further developments to our political system. You might also try /r/askphilosophy, as again, its been ages, but he is seen as a neo-Hegelian, and is basically using Hegel's Historical Dialectic. So asking about that in relation to Hegel and Marx (Some might say Marx made a similar argument, with Communism being the "End of History") would be a good approach to this question.