Lyrics: Elisha Hoffman, 1887.

Music: Anthony Showalter, 1887.

Theme: The eternal God is your refuge, And underneath are the everlasting arms. Deuteronomy 33:27

This Gaither Vocal Band performance is classic, especially with the harmonica:

Or if you prefer, here’s Chet Atkins on guitar and Carman doing the singing.

Or the blogger at Subversive Influence has Mahalia Jackson.

What a fellowship, what a joy divine,
Leaning on the everlasting arms;
What a blessedness, what a peace is mine,
Leaning on the everlasting arms.

Refrain:
Leaning, leaning, safe and secure from all alarms;
Leaning, leaning, leaning on the everlasting arms.

Oh, how sweet to walk in this pilgrim way,
Leaning on the everlasting arms;
Oh, how bright the path grows from day to day,
Leaning on the everlasting arms.

What have I to dread, what have I to fear,
Leaning on the everlasting arms?
I have blessed peace with my Lord so near,
Leaning on the everlasting arms.

The story is that Mr. Showalter wrote the chorus to this hymn after an appeal for comfort from two separate friends whose wives (or perhaps close friends?) had died. He then sent his lyrics to Elisha Hoffman who penned the verses.

Sources:
Leaning on the Everlasting Arms by Deborah Macomber.