Several words, one spelling
The origin of the word till is not a single trail. In modern English the same four letters do unrelated work. As a preposition or conjunction, till means up to a given time, and it can usually replace until. As a verb, it means to prepare soil for crops. As a shop noun, it is the drawer or register that holds cash. In geology, it is the mixed clay, sand, pebbles, and boulders a glacier leaves behind. Those senses did not grow from one root that slowly split. They are separate histories that happen to look alike.
The time-word is the one that attracts a false story. Many speakers treat till as a clipped until, and they write 'til or 'till as if letters had been dropped. The record runs the other way.
A northern preposition
Till is the older English form. In northern Old English, especially in Northumbrian, til already meant to. Old Norse used til as the ordinary preposition for to, toward, and up to, where southern English kept to. Contact with Scandinavian speech in the north brought that usage into English. Historical dictionaries treat the preposition as a borrowing from early Scandinavian. Other handbooks leave room for a native northern form at least akin to the Norse word. The geography is not in dispute: this till starts in the north.
Until is the later, reinforced shape. It is recorded from about 1200, built by adding to till the prefix un- that also appears in unto. That prefix comes from Old Norse und, as far as or up to, from a Germanic family that includes Old English oð. The two halves of until say nearly the same thing: up to, plus up to. Swedish intill and Danish indtil are similar compounds. German bis is another doubled direction-word, though from different pieces. Until is therefore till with an extra prefix, not the source of till.
As a conjunction meaning to the time when, till appears by late Old English; its use as a full temporal subordinator is clearer in early Middle English. For a long time it could still mark space as well as time, the way Scandinavian til still can. That spatial use faded in English, and till settled as a time marker.
Frequency later reversed the etymology in people's minds. In the eighteenth century till grew rare in elevated prose. From about 1800 until rose steadily and, in present-day English, overtook till even in speech. Many style notes still prefer until at the beginning of a sentence, though the two remain interchangeable in most positions. The spelling 'till became fashionable in the 1700s, as if till were a shortening; it is now treated as nonstandard. The later 'til is used, but it is etymologically a mistake.
Aim, then soil
The farm verb is a different English word, inherited from Old English tilian. That verb first meant to strive after, to exert oneself to obtain something. It broadened to work at a task, then narrowed to tend land. By the early thirteenth century it is used of cultivating crops; by the late fourteenth it can mean to plow. Figurative tilling follows soon after.
The verb is related to Old English til, good, useful, or suitable, and to a noun till meaning a fixed point or goal. Behind both the time-preposition and the farm verb is a Germanic idea of direction toward a mark. Linguists reconstruct a Proto-Germanic noun *tilan or *tilą, a planned point or aim. Icelandic tili still means scope or purpose; aldrtili is death, literally the end of life. German Ziel is a goal or limit. Gothic tils meant convenient or fitting. On the verb side, Old Frisian tilia meant to get or cultivate, Dutch telen means to breed or raise, and German zielen means to aim. English till as a farm verb is native, not a loan of the Norse preposition, but the two share that older notion of heading toward a point.
The shift from striving to plowing is ordinary, not mysterious. A language that already talks about working land as simply working will let a general labor verb settle on agriculture. Old Norse yrkja and Church Slavonic delati show a similar narrowing from work to cultivate. Once English till meant prepare soil, later forms such as tillage, tilth, and untilled could ride that sense without keeping the older meaning of aspiration.
A drawer, then a glacier
The cash till is yet another word, and its source is uncertain. It is first recorded in Middle English in the mid-fifteenth century, with one standard historical dictionary dating the earliest evidence to 1452. At that stage it was a locker, casket, or closed compartment inside a chest, used for valuables of any kind. Only in the 1690s does it specialize as the money box or drawer under a shop or bank counter. From that drawer it became the removable tray in a cash register, the register itself, and the money kept there. To have one's fingers in the till is to steal from that store.
Proposed sources do not agree. One line points to Anglo-French tylle, a compartment, and Old French tille, a compartment or a shelter on a ship, perhaps from Old Norse þilja, a plank or floorboard. Another derives the noun from Middle English tillen, to draw or pull, by the same kind of shift that produced drawer from draw. A further suggestion looks to Anglo-Latin attillium, equipment, and Middle English atil. None of those accounts is secure, and none ties the money box to plowing a field.
Geologists added a fourth till in 1765, first in Scottish use: unconsolidated, mixed clay, sand, pebbles, cobbles, and boulders dumped by ice. That sense also has no demonstrated link to the time-word or the verb. Its origin is unknown.
The apostrophe is the latecomer
The fact worth keeping is simple. Till as a time-word is older than until and was never a contraction of it. The apostrophe in 'til is a later fiction. The farm verb grew from the same Germanic idea of an aim, but along a native Old English path. The shop drawer and the glacial rubble only look related because English spelling folded several histories into four letters.