Luke 1:26-31: "26 In the sixth month the angel Gabriel was sent from God to a city of Galilee named Nazareth, 27 to a virgin betrothed to a man whose name was Joseph, of the house of David. And the virgin's name was Mary. 28 And he came to her and said, 'Greetings, O favored one, the Lord is with you!' 29 But she was greatly troubled at the saying, and tried to discern what sort of greeting this might be. 30 And the angel said to her, 'Do not be afraid, Mary, for you have found favor with God. 31 And behold, you will conceive in your womb and bear a son, and you shall call his name Jesus.'"
Luke 2:7-11: "7 And she gave birth to her firstborn son and wrapped him in swaddling cloths and laid him in a manger, because there was no place for them in the inn.
"8 And in the same region there were shepherds out in the field, keeping watch over their flock by night. 9 And an angel of the Lord appeared to them, and the glory of the Lord shone around them, and they were filled with fear. 10 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. 11 For unto you is born this day in the city of David a Savior, who is Christ the Lord.'"
Psalm 95:1-6: "1 Oh come, let us sing to the LORD; let us make a joyful noise to the rock of our salvation! 2 Let us come into his presence with thanksgiving; let us make a joyful noise to him with songs of praise! 3 For the LORD is a great God, and a great King above all gods. 4 In his hand are the depths of the earth; the heights of the mountains are his also. 5 The sea is his, for he made it, and his hands formed the dry land. 6 Oh come, let us worship and bow down; let us kneel before the LORD, our maker!"
Philippians 2:5-7: "5 Have this mind among yourselves, which is yours in Christ Jesus, 6 who, though he was in the form of God, did not count equality with God a thing to be grasped, 7 but made himself nothing, taking the form of a servant, being born in the likeness of men."
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The text is public domain:
From east to west, from shore to shore
Let ev'ry heart awake and sing
The holy child whom Mary bore,
The Christ, the everlasting king.
Behold, the world's creator wears
The form and fashion of a slave;
Our very flesh our maker shares,
His fallen creatures all to save.
For this how wondrously He wrought!
A maiden, in her lowly place,
Became, in ways beyond all thought,
The chosen vessel of His grace.
And while the angels in the sky
Sang praise above the silent field,
To shepherds poor the Lord Most High,
The one great Shepherd, was revealed.
All glory for this blessed morn
To God the Father ever be;
All praise to You, O Virgin-born,
And Holy Ghost eternally.
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The beginning of the first verse seems to come from Psalm 95, but there isn't much resemblance as far as specific word choice. The distance between "the depths of the earth [and] the heights of the mountains" and between "the sea" and "the dry land" seems to be what the hymn references in the line "From east to west, from shore to shore." Both Psalm 95 and this first verse also invite us to "sing to the LORD."
The hymn's second verse comes from the Philippians text. Christ's "taking the form of a servant [and] being born in the likeness of men" is rendered as: "the world's creator wears / The form and fashion of a slave; / Our very flesh our maker shares."
The third and fourth verses come from the two sections of Luke that are cited. The third verse (God's choosing Mary) is from Luke 1:26-31, and the fourth verse (the angel's announcing Jesus' birth to the shepherds) from Luke 2:7-11.