I ran Google searches for "one hundred one" and "one hundred and one" for the period 1600–1900. Many of the matches are false positives—but among the valid ones, "one hundred and one" appears more frequently and from a much earlier date.
The earliest match for "one hundred and one" is from the fascinatingly titled An Historical Essay: Endeavoring a Probability That the Language of the Empire of China is the Primitive Language (1669), by "John Webb of Butleigh in the County of Somerset Esquire":
We well know, those are not wanting, that make Nimrod to have arrived at Shinaar in the year one hundred and one after the Flood, and the Confusion [of Tongues] to have been at Phaleg's birth ; but although it is not to be believed; as Vossius saith, that the building of the Tower [of Babel], the Confusion of Tongues, and dispersion of the people should be made, before scarcely one Age after the Deluge was expired ; and though, as Sir W. Raleigh tells us "These men do all by miracle, an beget whole Nations without the help of Time["] ; nevertheless let it be as improbable, and the time as much abridged as it will, even by this computation also, the Classique History of the Chinois begins fourteen years before the Confusion of Tongues happened.
The earliest match for "one hundred and one" preceding a noun is from "Several Clauses in an Act, Intituled, An Act for making good the Deficiencies of several Fonds therein mentioned; and for Enlarging the Capital Stock of the Bank of England ; and for Raising the Publick Credit" enacted in "Anno 8 & 9 Gulielmi III Regis" (that is, in 1697 or 1698), reproduced in The Act of Tonnage and Poundage, and Rates of Merchandize (1702):
... upon the said Fourth Aid of four Shillings in the pound, Nine hundred and seventeen thousand one hundred and one pounds, Thirteen shillings, and Two pence half-peny ; ...
The earliest Google Books match for "one hundred one," meanwhile, is from Elias Voster, Arithmetic, in Whole and Broken Numbers, Digested after a New Method, and Chiefly Adapted for the Trade of Ireland, thirteenth Edition (1774):
Of Numbers consisting of Six Figures.
Write down, viz.
Four hundred seventy three thousand one hundred one _ _ _ _ _ _ _ _ _ [Answer]
Of Numbers consisting of Eight Figures.
Put down the following Sums, viz.
Forty millions one hundred eleven thousand one hundred one _ _ _ _ _ _ _ _ _ [Answer]
And the earliest match for "one hundred one" preceding a noun is from a lengthy series of tax tables included in "An act to authorize the Portland Union Railway Company to divide their stock into shares of less than one hundred dollars each" (March 16, 1860), in Acts and Resolves Passed by the Thirty-Ninth Legislature of the State of Maine (1860):
Presque Isle, One hundred one dollars, fifty five cents, $101 55
Edmunds, One hundred one dollars, thirteen cents, 101 13
On the evidence of these (and other early) Google Books search results, it appears that "one hundred and one" was in use by the second half of the 1600s and that "one hundred one" was in use by the second half of the 1700s.