He is from the sewers of Zaun...
http://leagueoflegends.wikia.com/wiki/Twitch/Background
Its pretty obvious when you hear his quotes towards other champs from Zaun:
http://vignette2.wikia.nocookie.net/leagueoflegends/images/8/8e/Twitch.tauntZac01.ogg/revision/latest?cb=20140404225440
http://vignette2.wikia.nocookie.net/leagueoflegends/images/2/28/Twitch.tauntSinged01.ogg/revision/latest?cb=20140404225439
If a champ has dangerous technology and/or toxic abilities, he/she is ususally from Zaun.
Here is his old lore if you want to learn more about the Rat... its not canon anymore, but helps:
The city-state of Zaun is a twisted realm of science, mercantilism, and magic run amok. While the young science of techmaturgy does much to advance civilization, its research and use in Zaun pushes the boundaries of morality on a daily basis. Zaun, choked with pollution from the countless factories and laboratories that spew waste into the environment, suffers greatly. As polluted as Zaun is above-ground, its subterranean levels are far worse. All of Zaun's runoff waste pooled together in its sewers, mixing into a toxic and mysterious concoction. A single plague rat rose from this alchemical nightmare - Twitch. Unlike his lesser evolved cousins, Twitch became as sentient as anyone else... provided they were as insane as he. A seeming byproduct of the evolutionary brew that spawned him was maniacal insanity, albeit in a functional form.
Twitch came to the League of Legends to represent himself "as the only one of his kind" on the Fields of Justice. Since then, he has found a generous benefactor in the city that gave him his evolutionary sentience - Zaun. Twitch is one of Zaun's premier champions in the League, and as such he fights for Zaun when political disputes between Valoran's city-states arise. Twitch has publicly stated that his goal is to gain enough influence and material from his work in the League to try to recreate the process by which he gained his sentience. While many challenges lie ahead in his quest - one of the largest being his own insanity - were he to succeed, it would mean a bold and brazen step forward in the evolution of all of Runeterra. Zaun has pledged its support for Twitch in his quest, though it remains to be seen what Zaun's ulterior motives are in the matter.
"The existence of Twitch proves that anything is possible on Runeterra."
― Heimerdinger
