Lin in Kansas gave the early history of "Old Hundredth" Here is a little more on this famous old song.
The tune was given English words and published in a psalter (Book of psalms) prepared by Henry Ainsworth and published in Amsterdam in 1612. The Ainsworth Psalter and the Bible were the only books the pilgrims brought with them when they came to America from Holland.
Longfellow, in "The Courtship of Miles Standish," describes Priscilla-

"Open wide on her lap lay the well-worn psalm-book of Ainsworth, Printed in Amsterdam, the words and the music together,
Rough-hewn angular notes, like stones in the wall of a churchyard,
Darkened and overhung by the running vine of the verses."

Words to the first verse differ from those given in Cyberhymnal, (Kethe's words from the Genevan Psalter and copied in the Ainsworth Psalter):

All people that on earth do dwell,
Sing to the Lord with cheerful voice.
Serve Him with mirth, His praise forth tell;
Come ye before Him and rejoice.

'Mirth,' not 'fear'

Thomas Ken, 1709 (1674?), wrote these well-known words to the Old Hundredth (Doxology) (the last verse of his longer hymn, "Awake, My Soul, and With the Sun"), using the Bourgeois tune from the Genevan Psalter:

Praise God, from whom all blessings flow;
Praise Him all creatures here below;
Praise Him above, ye heav'nly host;
Praise Father, Son, and Holy Ghost.

Seeger did an excellent job. Do we need another slight revision for today?