Luke 2:10-14: "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. 12 And this will be a sign for you: you will find a baby wrapped in swaddling cloths and lying in a manger.' 13 And suddenly there was with the angels a multitude of the heavenly host praising God and saying, 14 'Glory to God in the highest, and on earth peace among those with whom he is pleased!'"
Luke 2:20: "And the shepherds returned, glorifying and praising God for all they had heard and seen, as it had been told them."
Luke 1:46-47: "46 And Mary said, 'My soul magnifies the Lord, 47 and my spirit rejoices in God my Savior.'"
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The text is public domain:
Rejoice, rejoice this happy morn,
A Savior unto us is born,
The Christ, the Lord of glory!
His lowly birth in Bethlehem
The angels from on high proclaim
And sing redemption's story!
My soul, extol
God's great favor;
Bless Him ever
For salvation;
Give Him praise and adoration!
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This hymn consists of a single verse, so the Biblical sources are pretty easy to trace. Luke 2:10-14 is the source for the first half of the hymn, although "A Savior unto us is born" bears some resemblance to the first part of Isaiah 9:6: "For to us a child is born...." "My soul, extol / God's great favor" is from Luke 1:46 (the beginning of the Magnificat). Finally, "Give Him praise and adoration" comes from Luke 2:20. For these last two (Luke 1:46 and 2:20), the Biblical sources are in the indicative mood, but the hymn shifts them into the imperative.