Luke 2:10-20: "And the angel said to them, 'Fear not, for behold, I bring you good news of great joy that will be for all the people. For unto you is born this day in the city of David a Savior, who is Christ the Lord. And this will be a sign for you: you will find a baby wrapped in swaddling cloths and lying in a manger.' And suddenly there was with the angel a multitude of the heavenly host praising God and saying, 'Glory to God in the highest, and on earth peace among those with whom he is pleased!'
"When the angels went away from them into heaven, the shepherds said to one another, 'Let us go over to Bethlehem and see this thing that has happened, which the Lord has made known to us.' And they went with haste and found Mary and Joseph, and the baby lying in a manger. And when they saw it, they made known the saying that had been told them concerning this child. And all who heard it wondered at what the shepherds told them. But Mary treasured up all these things, pondering them in her heart. And the shepherds returned, glorifying and praising God for all they had heard and seen, as it had been told them."
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The text is public domain:
"From heav'n above to earth I come
To bear good news to ev'ry home;
Glad tidings of great joy I bring,
Whereof I now will say and sing:
"To you this night is born a child
Of Mary, chosen virgin mild;
This little child of lowly birth
Shall be the joy of all the earth.
"This is the Christ, our God Most High,
Who hears your sad and bitter cry;
He will Himself your Savior be
From all your sins to set you free.
"He will on you the gifts bestow
Prepared by God for all below,
That in His kingdom, bright and fair,
You may with us His glory share.
"These are the signs that you shall mark:
The swaddling clothes and manger dark.
There you will find the infant laid
By whom the heav'ns and earth were made."
How glad we'll be to find it so!
Then with the shepherds let us go
To see what God for us has done
In sending us His own dear Son.
Come here, my friends, lift up your eyes,
And see what in the manger lies.
Who is this child, so young and fair?
It is the Christ Child lying there.
Welcome to earth, O noble Guest,
Through whom the sinful world is blest!
You came to share my misery
That You might share Your joy with me.
Ah, Lord, though You created all,
How weak You are, so poor and small,
That You should choose to lay Your head
Where lowly cattle lately fed!
Were earth a thousand times as fair
And set with gold and jewels rare,
It would be far too poor and small
A cradle for the Lord of all.
Instead of soft and silken stuff
You have but hay and straw so rough
On which as King, so rich and great,
To be enthroned in royal state.
And so it pleases You to see
This simple truth revealed to me:
That worldly honor, wealth, and might
Are weak and worthless in Your sight.
Ah, dearest Jesus, holy Child,
Prepare a bed, soft, undefiled,
A quiet chamber set apart
For You to dwell within my heart.
My heart for very joy must leap;
My lips no more can silence keep.
I, too, must sing with joyful tongue
That sweetest ancient cradlesong:
Glory to God in highest heav'n,
Who unto us His Son has giv'n!
While angels sing with pious mirth
A glad new year to all the earth.
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Because there's only one Biblical text cited, it's obvious that that's the main referent for the hymn text, but I found a few other Biblical texts that are hinted at.
The lines "There you will find the infant laid / By whom the heav'ns and earth were made" at the end of verse five brought to mind John 1:3: "All things were made through him, and without him was not any thing made that was made."
The lines "Come here, my friends, lift up your eyes" and "Who is this child, so young and fair? / It is the Christ Child lying there" in the seventh verse echo Psalm 121:1-2: "I lift up my eyes to the hills. From where does my help come? My help comes from the LORD, who made heaven and earth." Both begin with "lift[ing] up... eyes" and then ask a rhetorical question to which God is the answer.
The fourteenth verse begins with "My heart for very joy must leap," which - although it stands by itself - also describes Luke 1:39-45, where John the Baptist "leaped for joy" when Mary came to visit Elizabeth.