Wordorigins.org

These are simply nonsense words used in various children’s counting-out rhymes. The words have no intrinsic significance and variants are found in several different languages. There is no canonical version and a great number of variations on the rhyme are found.

The oldest known versions date to 1855 and are found in the publication Notes & Queries:

The Schoolboy Formula...Eeny, meeny, moany, mite...Eeny, meeny, tipty, te.