The tune was not associated with Psalm 100 until the publication of the 1561 Anglo-Genevan Psalter (Four Score and Seven Psalms of David). It was employed along with an arrangement of this psalm by William Kethe, although initially ascribed to Sternhold & Hopkins. The tune was also used in the same psalter with a versification of the Lord's Prayer by William Whittingham. It took the name "Old 100th" later to distinguish from the "new" Psalter by Tate and Brady.
One may enjoy listening to the tune and reading the lyrics to 'All People That on Earth Do Dwell' here (note that the last stanza is a doxology and not part of Psalm 100).
Lewis Lupton, A History of the Geneva Bible, Vol. 5 (1973), pp. 87-88:
The most interesting feature of this edition [ie., the 1561 edition of the Anglo-Genevan Psalter] is the inclusion for the first time of the Old Hundredth 'All people that on earth do dwell'. Surprisingly enough it is under the signature of Tho. Ster:
The explanation is that Kethe translated this psalm (which was written to fit a tune composed by Louis Bourgeois for psalm 134 in Beza's Psalter of 1551) after he had left Geneva in 1560 on his way to Britain....In the English black letter edition [a copy of the 1561 Anglo-Genevan Psalter printed in England rather than Geneva] the hundredth psalm is attributed to Kethe (Psalme C. W.Ke.) at the foot of the previous page to that on which the psalm begins which is, of course, the reason the Genevan printers failed to notice the author's name and substituted the most likely one they could think of.
As far as the tune of the 'Old Hundredth' is concerned, its introduction into Britain would appear to be due to Whittingham as well as Kethe.