"give a small present of money to," c. 1600, originally "to give, hand, pass," thieves' cant, perhaps from tip (v.3) "to tap." The meaning "give a gratuity to" is first attested 1706. The noun in this sense is from 1755; the noun meaning "piece of confidential information" is from 1845; and the verb in the sense "give private information to" is from 1883.
The popularity of the tale of the word's supposed origin as an acronym in mid-18th century English taverns seems to be no older than Frederick W. Hackwood's 1909 book "Inns, Ales and Drinking Customs of Old England," where it was said to stand for To insure promptitude (in the form to insure promptness the anecdote is told from 1946). A reviewer of the book in the "Athenaeum" of Oct. 2, 1909, wrote, "We deprecate the careless repetition of popular etymologies such as the notion that "tip" originated from an abbreviated inscription on a box placed on the sideboard in old coaching-inns, the full meaning of which was "To Insure Promptitude." Also see here.