Augustine of Hippo and other Christian theologians formalized it, but the conceptual root of the doctrine of original sin is an integral part of the teachings of Paul of Tarsus:
Without Adam's fall "mysteriously" affecting the nature of all humans, there's no need for redemption through the risen Christ, according to Pauline theology. Augustine of Hippo and others merely developed this original thread into a full-bodied doctrine.
It should be said that before Paul of Tarsus, Jewish religious scholars attached little or no importance to Adam's sin; and the notion of "original sin" is totally alien to Judaism. Most probably, Paul developed on his own an ancient idea, present in ancient Judaism and ancient polytheist religions (both Semitic and Graeco-Roman) that the son inherited the sin of the father, and that of collective guilt and collective punishment by the gods (or YHWH). Although in doing so he was shooting himself in the foot by downgrading the notion of divine Justice and the value of the Last Judgement as the trial of an individual soul by God for his/her own sins. There's a good reason why neither Judaism, nor Islam, nor some Christian churches ever accepted this notion.
It makes perfect sense from the historical context (at least for Paul) the Jew were living in a Jewish state, the Muslims were living in an Islamic state. Thus there is no conflict between earthly/secular and heavenly/canon law. Early Christians were living in a non-Christian state, thus they needed an "excuse" why they are not purists. An the concept of original sins (no matter what you do you have sins) and the redemption through the belief in Christ offered exactly that. It was also allowed greater reach for the missionary work, since suddenly all men become equal irrespective of their actions and characters.
(later on they had to refine the thing when they become the ruling elite)