As per Etymonline:
Used from 16c. in adjectival sense of "utter, absolute, quite" (cf. dead drunk first attested 1590s; dead heat, 1796). As an adverb, from late 14c. Dead on is 1889, from marksmanship.
I'm sure that someone with OED access can provide a complete answer with some citations.
If you consider someone shooting on a mark (at a target), then dead on could be considered an elision of dead on the mark. In other words, completely on target. A similar expression would be dead on the money.
According to one online source:
For prize competitions in [sic] a coin would be set at the middle of the target and the archer whose arrow landed closest to the coin would take the coin as the prize.
Therefore right on the money would mean the center of the target (dead center).
Practice of shooting the coin with arrows is still used today.
[Link to archery event where coins are shot at]
DERIVATION: This expression derives from an old English sport, bullbaiting dogs try to pull a bull by his nose to the ground. Gamblers would place a bet "on the bull's eye" if he wished to make a bet. Crowns, an English coin, were used to bet so frequently "on the bull's eye" that the coin itself came to be called a bull's-eye. Later, the term was applied to the black center of a target. The idiom right on the money is also derived from the ancient interchangeable use of a coin, bull's-eye and the center of a target.
A few more details about the word dead in this and similar phrases is found in this ELU question.