John 5:24: "'Truly, truly, I say to you, whoever hears my word and believes him who sent me has eternal life. He does not come into judgement, but has passed from death to life.'"
1 Corinthians 15:51-57: "51 Behold! I tell you a mystery. We shall not all sleep, but we shall all be changed, 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. 53 For this perishable body must put on the imperishable, and this mortal body must put on immortality. 54 When the perishable puts on the imperishable, and the mortal puts on immortality, then shall come to pass the saying that is written: 'Death is swallowed up in victory.' 55 'O death, where is your victory? O death, where is your sting?' 56 The sting of death is sin, and the power of sin is the law. 57 But thanks be to God, who gives us the victory through our Lord Jesus Christ."
2 Corinthians 5:4: "For while we are still in this tent, we groan, being burdened - not that we would be unclothed, but that we would be further clothed, so that what is mortal may be swallow up by life."
1 Thessalonians 4:13-14: "13 But we do not want you to be uninformed, brothers, about those who are asleep, that you may not grieve as others do who have no hope. 14 For since we believe that Jesus died and rose again, even so, through Jesus, God will bring with him those who have fallen asleep."
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The text is public domain:
1 This body in the grave we layThere to await that solemn dayWhen God Himself shall bid it riseTo mount triumphant to the skies.2 And so to earth we now entrustWhat came from dust and turns to dustAnd from the dust shall rise that dayIn glorious triumph o'er decay.3 The soul forever lives with God,Who freely hath His grace bestowedAnd through His Son redeemed it hereFrom ev'ry sin, from ev'ry fear.4 All trials and all griefs are past,A blessed end has come at last.Christ's yoke was borne with ready will;Who dieth thus is living still.5 We have no cause to mourn or weep;Securely shall this body sleepTill Christ Himself shall death destroyAnd raise the blessed dead to joy.6 Then let us leave this place of restAnd homeward turn, for they are blestWho heed God's warning and prepareLest death should find them unaware.7 So help us, Jesus, ground of faith;Thou hast redeemed us by Thy deathFrom endless death and set us free.We laud and praise and worship Thee.
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All of the cited passages inform the hymn (especially the fifth verse) in a more general way. The passage from 1 Corinthians 15 seems to be alluded to in the phrase "glorious triumph o'er decay" at the end of the second verse, and John 5:24 seems to be the basis for most of the seventh verse.
The line "What came from dust and turns to dust" in the second verse could refer to either Ecclesiastes 3:20 ("All go to one place. All are from the dust, and to dust all return.") or part of Genesis 3:19 ("'for you are dust, and to dust you shall return'").