Isaiah 26:3: "You keep him in perfect peace whose mind is stayed on you, because he trusts in you."
Luke 2:29: "'Lord, now you are letting your servant depart in peace, according to your word'"
Romans 5:1: "Therefore, since we have been justified by faith, we have peace with God through our Lord Jesus Christ."
Colossians 3:15: "And let the peace of Christ rule in your hearts, to which indeed you were called in one body. And be thankful."
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The text is public domain:
1 When peace, like a river, attendeth my way;When sorrows, like sea billows, roll;Whatever my lot, Thou hast taught me to say,It is well, it is well with my soul.It is well with my soul,It is well, it is well with my soul.2 Though Satan should buffet, though trials should come,Let this blest assurance control,That Christ hath regarded my helpless estateAnd hath shed His own blood for my soul.It is well with my soul,It is well, it is well with my soul.3 He lives - oh, the bliss of this glorious thought;My sin, not in part, but the whole,Is nailed to His cross, and I bear it no more.Praise the Lord, praise the Lord, O my soul!It is well with my soul,It is well, it is well with my soul.4 And, Lord, haste the day when our faith shall be sight,The clouds be rolled back as a scroll,The trumpet shall sound and the Lord shall descend;Even so it is well with my soul.It is well with my soul,It is well, it is well with my soul.
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All of the cited passages mention peace, which appears in the first line and more generally in the refrain. Romans 5:1 may also appear (but only generally) in the second and third verses. The simile in the title line ("peace, like a river") seems to come from part of Isaiah 66:12: "For thus says the LORD: 'Behold, I will extend peace to her like a river, and the glory of the nations like an overflowing stream....'"
Parts of the fourth verse come from Revelation 6:14 ("The sky vanished like a scroll that is being rolled up, and every mountain and island was removed from its place.") and 1 Corinthians 15:52 ("in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised imperishable, and we shall be changed.").