It has been set to at least three hymn tunes:
In the latter half of the twentieth century the hymn was popularized as an altar call song in the Billy Graham crusades. Graham used the title of the hymn as the title of his 1997 autobiography (ISBN 0-06-063387-5).
An elderly man asked Charlotte Elliott if she were a Christian; she felt insulted, and told him to mind his own affairs. But after the man left, she could not get the question off her mind, and she went back to ask the man how to find Christ. He told her to come just as she was. She did, and wrote the beautiful song, "Just As I Am." - By B. A. Scherr
2.
Just as I am, and waiting not
To rid my soul of one dark blot,
To Thee whose blood can cleanse each spot,
O Lamb of God, I come, I come.
3.
Just as I am, tho' tossed about
With many a conflict, many a doubt,
Fightings and fears within, without,
O Lamb of God, I come, I come.
4.
Just as I am, poor, wretched, blind-
Sight, riches, healing of the mind,
Yea, all I need in Thee to find-
O Lamb of God, I come, I come.
5. Just as I am, of that free love
The breadth, length, depth and height to prove,
Here for a season, then above,
O Lamb of God, I come.
Just as I am, Thou wilt receive,
Wilt welcome, pardon, cleanse, relieve,
Because Thy promise I believe,
O Lamb of God, I come! I come!
Source: Signs of the Times, Copyright (c) July 26, 1942, Pacific Press.
Other sources are different: Each verse ends only with a single "I come." (otherwise the hymns would not scan), omit verse 2 above and add two additional verses: