Zechariah 9:9: "Rejoice greatly, O daughter of Zion! Shout aloud, O daughter of Jerusalem! Behold, your king is coming to you; righteous and having salvation is he, humble and mounted on a donkey, on a colt, the foal of a donkey."
Luke 2:14: "'Glory to God in the highest, and on earth peace among those with whom he is pleased!'"
John 14:18: "'I will not leave you as orphans; I will come to you.'"
Matthew 25:31-34: "'When the Son of Man comes in his glory, and all the angels with him, then he will sit on his glorious throne. Before him will be gathered all the nations, and he will separate people one from another as a shepherd separates the sheep from the goats. And he will place the sheep on his right, but the goats on the left. Then the King will say to those on his right, "Come, you who are blessed by my Father, inherit the kingdom prepared for you from the foundation of the world."'"
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The text is public domain:
Jesus came, the heav'ns adoring,
Came with peace from realms on high;
Jesus came to win redemption,
Lowly came on earth to die;
Alleluia! Alleluia!
Came in deep humility.
Jesus comes again in mercy
When our hearts are worn with care;
Jesus comes again in answer
To an earnest, heartfelt prayer;
Alleluia! Alleluia!
Comes to save us from despair.
Jesus comes to hearts rejoicing,
Bringing news of sins forgiv'n;
Jesus comes with words of gladness,
Leading souls redeemed to heav'n.
Alleluia! Alleluia!
Hope to all the world is giv'n.
Jesus comes in joy and sorrow,
Shares alike our hopes and fears;
Jesus comes, whate'er befalls us,
Cheers our hearts and dries our tears;
Alleluia! Alleluia!
Comforts us in failing years.
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The lowliness and humility mentioned in the first verse are from the Zechariah text, and since that's a prophecy of Jesus' entrance into Jerusalem, those New Testament accounts (Matthew 21:1-16, Mark 11:1-11, and Luke 19:28-40) are also relevant.
The line "Came with peace from realms on high" from the same verse seems to be from the Luke 2 text, which is an excerpt from the angel's announcement of Jesus' birth to the shepherds.
The lines "Jesus comes with words of gladness, / Leading souls redeemed to heav'n" from the third verse refer to the Matthew 25 text.
I don't think the cited text from John shows up in any specific line in the hymn; rather, I think the "I will come to you" part is what the hymn constantly returns to. There are twelve phrases in which some form of "Jesus comes" appear:
- Jesus came, the heav'ns adoring
- Came with peace from realms on high
- Jesus came to win redemption
- Lowly came on earth to die
- Came in deep humility
- Jesus comes again in mercy / When our hearts are worn with care
- Jesus comes again in answer / To an earnest, heartfelt prayer
- Comes to save us from despair
- Jesus comes to hearts rejoicing, / Bringing news of sins forgiv'n
- Jesus comes with words of gladness, / Leading souls redeemed to heav'n
- Jesus comes in joy and sorrow
- Jesus comes, whate'er befalls us
It's not cited in the hymnal, but I think the lines "Jesus comes again in answer / To an earnest, heartfelt prayer" come from Philippians 4:6-7: "Do not be anxious about anything, but in everything by prayer and supplication with thanksgiving let your requests be made known to God. And the peace of God, which surpasses all understanding, will guard your hearts and your minds in Christ Jesus." To some degree, it connects with an earlier line in the hymn: "[Jesus] came with peace."