I tried to find a video version to share that had a simple, genuine tone to it. This one comes closest. It's performed by an unnamed group of performers from a Washington-D.C.-area church called Capital Life Church (try not to be distracted by their little musical title sequence at the beginning).
The lyrics were written in Montreal (probably in 1862 or 1864) by William Ralph Featherston, apparently very soon after his conversion. He was only 16. He died eleven years later, shortly before he was to turn 27. The tune was composed, most likely in 1876, by Adoniram Judson Gordon, an American Baptist preacher and composer.
YouTube video "My Jesus, I Love Thee"
Lyrics*
My Jesus, I love Thee, I know Thou art mine;
For Thee all the follies of sin I resign.
My gracious Redeemer, my Savior art Thou;
If ever I loved Thee, my Jesus, ’tis now.
I love Thee because Thou has first loved me,
And purchased my pardon on Calvary’s tree.
I love Thee for wearing the thorns on Thy brow;
If ever I loved Thee, my Jesus, ’tis now.
I’ll love Thee in life, I will love Thee in death,
And praise Thee as long as Thou lendest me breath;
And say when the death dew lies cold on my brow,
If ever I loved Thee, my Jesus, ’tis now.
In mansions of glory and endless delight,
I’ll ever adore Thee in heaven so bright;
I’ll sing with the glittering crown on my brow;
If ever I loved Thee, my Jesus, ’tis now.
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* Lyrics source. Background story compiled from various sources, including this.